A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit sol...
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| Published in: | Journal of computational physics Vol. 257; no. Part A; pp. 594 - 626 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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United States
Elsevier Inc
15.01.2014
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| ISSN: | 0021-9991, 1090-2716 |
| Online Access: | Get full text |
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| Abstract | Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial.
Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation.
A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma. |
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| AbstractList | Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial.
Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation.
A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma. Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. In a prior paper we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma. Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation. A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma. Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes "s" explicit Runge-Kutta-like time-steps to advance the parabolic terms by a time-step that is s2s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge-Kutta scheme to the recursion relation of some well-known, stable polynomial. |
| Author | Meyer, Chad D. Aslam, Tariq D. Balsara, Dinshaw S. |
| Author_xml | – sequence: 1 givenname: Chad D. surname: Meyer fullname: Meyer, Chad D. organization: Physics Department, Univ. of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA – sequence: 2 givenname: Dinshaw S. surname: Balsara fullname: Balsara, Dinshaw S. organization: Physics Department, Univ. of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA – sequence: 3 givenname: Tariq D. surname: Aslam fullname: Aslam, Tariq D. organization: WX-9 Group, Los Alamos National Laboratory, MS P952, Los Alamos, NM 87545, USA |
| BackLink | https://www.osti.gov/biblio/22230848$$D View this record in Osti.gov |
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| Cites_doi | 10.1002/(SICI)1099-0887(199601)12:1<31::AID-CNM950>3.0.CO;2-5 10.1111/j.1365-2966.2008.13085.x 10.1016/j.jcp.2006.11.004 10.1137/090775804 10.1016/0021-9991(90)90097-K 10.1016/S0168-9274(96)00022-0 10.1109/T-ED.1985.22232 10.1086/381377 10.1007/BF02512373 10.1146/annurev.fluid.38.050304.092049 10.1137/0729053 10.1111/j.1365-2966.2012.20744.x 10.1016/j.jcp.2012.04.051 10.1006/jcph.1996.0145 10.1006/jcph.2000.6488 10.1111/j.1365-2966.2007.11429.x 10.1016/j.jcp.2008.12.003 10.1137/0705041 10.1111/j.1151-2916.1997.tb02790.x 10.1063/1.857961 10.1016/0168-9274(95)00109-3 10.1137/S1064827500379549 10.1007/s10915-007-9169-1 10.1002/zamm.19800601005 10.1007/s002850000038 10.1016/S0377-0427(97)00219-7 10.1007/BF01329605 10.1063/1.1724332 10.1016/0021-9991(88)90002-2 |
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| References | Meyer, Balsara, Aslam (br0370) 2012; 422 OʼSullivan, Downes (br0390) 2007; 376 LeVeque, Yee (br0330) 1990; 86 Tyson, Stern, LeVeque (br0490) 2000; 41 Verwer (br0530) 1996; 22 Osher, Sethian (br0410) 1988; 79 Weast (br0540) 1984 Balsara, Rumpf, Dumbser, Munz (br0110) 2009; 228 Barenblatt (br0150) 1952; 16 Markstein (br0340) 1964 Osher, Fedkiw (br0400) 2002; vol. 153 Gassner, Lörcher, Munz (br0190) 2007; 224 Hundsdorfer, Verwer (br0260) 2003 Rouy, Tourin (br0440) 1992; 29 Aslam, Jackson, Morris (br0070) 2009 van Der Houwen, Sommeijer (br0510) 1980; 60 Dumbser, Balsara (br0180) 2010; 54 Balsara, Tilley, Howk (br0100) 2008; 386 Lebedev (br0290) 1994 Sommeijer, Shampine, Verwer (br0470) 1998; 88 Abdulle (br0020) 2002; 23 Lee, Chung (br0310) 1997; 80 Balsara (br0090) 2004; 151 Vázquez (br0520) 2007 Marshak (br0350) 1958; 1 Gurski (br0220) 2011; vol. 1368 Aslam, Bdzil (br0050) 2002 Reinicke, Meyer-ter-Vehn (br0430) 1991; 3 Aslam, Bdzil (br0060) 2006 Lebedev (br0300) 2000; 40 Jackson (br0280) 1975 Rubenstein (br0450) 1971 Patankar (br0420) 1980 Strang (br0480) 1968; 5 Bank, Coughran, Fichtner, Grosse, Rose, Smith (br0130) 1985; ED-32 Hill, Aslam (br0240) 2003 Incropera, DeWitt (br0270) 1990 Hairer, Wanner (br0230) 1996; vol. 14 Abdulle (br0010) 2001 Gurski, OʼSullivan (br0210) 2011; 49 LeVeque (br0320) 1992 Mousseau, Knoll, Rider (br0380) 2000; 160 Balsara, Meyer, Dumbser, Du, Xu (br0120) 2013; 235 Sethian (br0460) 1999 Alexiades, Amiez, Gremaud (br0030) 1996; 12 Baer, Stephan (br0080) 2006 van der Houwen (br0500) 1996; 20 Gassner, Lörcher, Munz (br0200) 2008; 34 Bdzil, Stewart (br0160) 2007; 39 Becker (br0170) 1923; 8 Medovikov (br0360) 1998; 38 Hill, Aslam (br0250) 2010 Aslam, Bdzil, Stewart (br0040) 1996; 126 Aslam (10.1016/j.jcp.2013.08.021_br0070) 2009 Gassner (10.1016/j.jcp.2013.08.021_br0200) 2008; 34 Hairer (10.1016/j.jcp.2013.08.021_br0230) 1996; vol. 14 Hill (10.1016/j.jcp.2013.08.021_br0250) 2010 Osher (10.1016/j.jcp.2013.08.021_br0400) 2002; vol. 153 Rubenstein (10.1016/j.jcp.2013.08.021_br0450) 1971 Lebedev (10.1016/j.jcp.2013.08.021_br0290) 1994 Aslam (10.1016/j.jcp.2013.08.021_br0060) 2006 Gurski (10.1016/j.jcp.2013.08.021_br0210) 2011; 49 Vázquez (10.1016/j.jcp.2013.08.021_br0520) 2007 Rouy (10.1016/j.jcp.2013.08.021_br0440) 1992; 29 Reinicke (10.1016/j.jcp.2013.08.021_br0430) 1991; 3 Medovikov (10.1016/j.jcp.2013.08.021_br0360) 1998; 38 LeVeque (10.1016/j.jcp.2013.08.021_br0320) 1992 Markstein (10.1016/j.jcp.2013.08.021_br0340) 1964 Incropera (10.1016/j.jcp.2013.08.021_br0270) 1990 Balsara (10.1016/j.jcp.2013.08.021_br0090) 2004; 151 Gurski (10.1016/j.jcp.2013.08.021_br0220) 2011; vol. 1368 Aslam (10.1016/j.jcp.2013.08.021_br0050) 2002 Abdulle (10.1016/j.jcp.2013.08.021_br0010) 2001 Bank (10.1016/j.jcp.2013.08.021_br0130) 1985; ED-32 Marshak (10.1016/j.jcp.2013.08.021_br0350) 1958; 1 Patankar (10.1016/j.jcp.2013.08.021_br0420) 1980 LeVeque (10.1016/j.jcp.2013.08.021_br0330) 1990; 86 Hundsdorfer (10.1016/j.jcp.2013.08.021_br0260) 2003 Sethian (10.1016/j.jcp.2013.08.021_br0460) 1999 Bdzil (10.1016/j.jcp.2013.08.021_br0160) 2007; 39 Meyer (10.1016/j.jcp.2013.08.021_br0370) 2012; 422 Hill (10.1016/j.jcp.2013.08.021_br0240) 2003 Balsara (10.1016/j.jcp.2013.08.021_br0100) 2008; 386 van Der Houwen (10.1016/j.jcp.2013.08.021_br0510) 1980; 60 OʼSullivan (10.1016/j.jcp.2013.08.021_br0390) 2007; 376 Gassner (10.1016/j.jcp.2013.08.021_br0190) 2007; 224 Aslam (10.1016/j.jcp.2013.08.021_br0040) 1996; 126 Lebedev (10.1016/j.jcp.2013.08.021_br0300) 2000; 40 Lee (10.1016/j.jcp.2013.08.021_br0310) 1997; 80 Alexiades (10.1016/j.jcp.2013.08.021_br0030) 1996; 12 Dumbser (10.1016/j.jcp.2013.08.021_br0180) 2010; 54 Balsara (10.1016/j.jcp.2013.08.021_br0120) 2013; 235 Verwer (10.1016/j.jcp.2013.08.021_br0530) 1996; 22 van der Houwen (10.1016/j.jcp.2013.08.021_br0500) 1996; 20 Tyson (10.1016/j.jcp.2013.08.021_br0490) 2000; 41 Jackson (10.1016/j.jcp.2013.08.021_br0280) 1975 Barenblatt (10.1016/j.jcp.2013.08.021_br0150) 1952; 16 Strang (10.1016/j.jcp.2013.08.021_br0480) 1968; 5 Balsara (10.1016/j.jcp.2013.08.021_br0110) 2009; 228 Becker (10.1016/j.jcp.2013.08.021_br0170) 1923; 8 Sommeijer (10.1016/j.jcp.2013.08.021_br0470) 1998; 88 Mousseau (10.1016/j.jcp.2013.08.021_br0380) 2000; 160 Osher (10.1016/j.jcp.2013.08.021_br0410) 1988; 79 Baer (10.1016/j.jcp.2013.08.021_br0080) 2006 Abdulle (10.1016/j.jcp.2013.08.021_br0020) 2002; 23 Weast (10.1016/j.jcp.2013.08.021_br0540) 1984 |
| References_xml | – year: 2007 ident: br0520 article-title: The Porous Medium Equation: Mathematical Theory – volume: 80 year: 1997 ident: br0310 article-title: Ignition phenomena and reaction mechanisms of the self-propagating high-temperature synthesis reaction in the titanium–carbon–aluminum system publication-title: J. Am. Ceram. Soc. – volume: 3 start-page: 1807 year: 1991 ident: br0430 article-title: The point explosion with heat conduction publication-title: Phys. Fluids A, Fluid Dyn. – volume: 1 start-page: 24 year: 1958 ident: br0350 article-title: Effect of radiation on shock wave behavior publication-title: Phys. Fluids (US) – volume: 38 start-page: 372 year: 1998 end-page: 390 ident: br0360 article-title: High order explicit methods for parabolic equations publication-title: BIT Numer. Math. – volume: 79 start-page: 12 year: 1988 end-page: 49 ident: br0410 article-title: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations publication-title: J. Comput. Phys. – volume: 20 start-page: 261 year: 1996 end-page: 272 ident: br0500 article-title: The development of Runge–Kutta methods for partial differential equations publication-title: Appl. Numer. Math. – volume: 228 start-page: 2480 year: 2009 end-page: 2516 ident: br0110 article-title: Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics publication-title: J. Comput. Phys. – volume: 40 start-page: 1729 year: 2000 end-page: 1740 ident: br0300 article-title: Explicit difference schemes for solving stiff problems with a complex or separable spectrum publication-title: Comput. Math. Math. Phys. – volume: 235 start-page: 934 year: 2013 ident: br0120 article-title: Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes – comparison with Runge–Kutta methods publication-title: J. Comput. Phys. – year: 2002 ident: br0050 article-title: Numerical and theoretical investigations on detonation-inert confinement interactions publication-title: Twelfth International Detonation Symposium – volume: 422 start-page: 2102 year: 2012 end-page: 2115 ident: br0370 article-title: A second-order accurate Super TimeStepping formulation for anisotropic thermal conduction publication-title: Mon. Not. R. Astron. Soc. – volume: vol. 153 year: 2002 ident: br0400 article-title: Level Set Methods and Dynamic Implicit Surfaces publication-title: Appl. Math. Sci., Applied Mathematical Sciences – volume: 386 start-page: 627 year: 2008 end-page: 641 ident: br0100 article-title: Simulating anisotropic thermal conduction in supernova remnants—I. Numerical methods publication-title: Mon. Not. R. Astron. Soc. – year: 2009 ident: br0070 article-title: Proton radiography of PBX 9502 detonation shock dynamics sandwich test publication-title: Fifteenth APS Conference on Shock Compression of Condensed Matter – volume: 160 start-page: 743 year: 2000 end-page: 765 ident: br0380 article-title: Physics-based preconditioning and the Newton–Krylov method for non-equilibrium radiation diffusion publication-title: J. Comput. Phys. – volume: 49 start-page: 368 year: 2011 end-page: 386 ident: br0210 article-title: A stability study of a new explicit numerical scheme for a system of differential equations with a large skew-symmetric component publication-title: SIAM J. Numer. Anal. – volume: 60 start-page: 479 year: 1980 end-page: 485 ident: br0510 article-title: On the internal stability of explicit, publication-title: Z. Angew. Math. Mech. – volume: 224 start-page: 1049 year: 2007 end-page: 1063 ident: br0190 article-title: A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes publication-title: J. Comput. Phys. – year: 2003 ident: br0260 article-title: Numerical Solution of Time-Dependent Advection–Diffusion Reaction Equations – volume: vol. 1368 start-page: 239 year: 2011 end-page: 242 ident: br0220 article-title: A stability and cost study of explicit and dyadic time stepping for stiff nonsymmetric problems publication-title: AIP Conf. Proc. – year: 2001 ident: br0010 article-title: Chebyshev methods based on orthogonal polynomials – volume: 151 start-page: 149 year: 2004 end-page: 184 ident: br0090 article-title: Second order accurate schemes for magnetohydrodynamics with divergence-free reconstruction publication-title: Astrophys. J. Suppl. Ser. – volume: 126 start-page: 390 year: 1996 end-page: 409 ident: br0040 article-title: Level set methods applied to modeling detonation shock dynamics publication-title: J. Comput. Phys. – year: 1990 ident: br0270 article-title: Introduction to Heat Transfer – start-page: 475 year: 1975 end-page: 479 ident: br0280 article-title: Classical Electrodynamics – volume: 23 start-page: 2041 year: 2002 end-page: 2054 ident: br0020 article-title: Fourth order Chebyshev methods with recurrence relation publication-title: SIAM J. Sci. Comput. – year: 1964 ident: br0340 article-title: Non-steady Flame Propagation – volume: 29 start-page: 867 year: 1992 end-page: 884 ident: br0440 article-title: A viscosity solutions approach to shape-from-shading publication-title: SIAM J. Numer. Anal. – year: 2006 ident: br0060 article-title: Numerical and theoretical investigations on detonation confinement sandwich tests publication-title: Thirteenth International Detonation Symposium – year: 2003 ident: br0240 article-title: The LANL detonation-confinement test: prototype development and sample results publication-title: Twelfth APS Conference on Shock Compression of Condensed Matter – volume: 16 start-page: 67 year: 1952 ident: br0150 article-title: On some unsteady motions of a liquid or a gas in a porous medium publication-title: Prikl. Mat. Meh. – volume: vol. 14 year: 1996 ident: br0230 article-title: Solving Ordinary Differential Equations II – Stiff and Differential Algebraic Problems publication-title: Springer Ser. Comput. Math. – volume: 12 start-page: 31 year: 1996 end-page: 42 ident: br0030 article-title: Super-time-stepping acceleration of explicit schemes for parabolic problems publication-title: Commun. Numer. Methods Eng. – year: 1980 ident: br0420 article-title: Numerical Heat Transfer and Fluid Flow – volume: 34 start-page: 260 year: 2008 end-page: 286 ident: br0200 article-title: A discontinuous Galerkin scheme based on a space–time expansion II. Viscous flow equations in multi dimensions publication-title: J. Sci. Comput. – volume: 54 start-page: 301 year: 2010 end-page: 334 ident: br0180 article-title: High-order unstructured one-step PNPM schemes for the viscous and resistive MHD equations publication-title: Comput. Model. Eng. Sci. – volume: 5 start-page: 506 year: 1968 end-page: 517 ident: br0480 article-title: On the construction and comparison of difference schemes publication-title: SIAM J. Numer. Anal. – start-page: 45 year: 1994 end-page: 80 ident: br0290 article-title: How to solve stiff systems of differential equations by explicit methods publication-title: Numer. Methods Appl. – volume: 86 start-page: 187 year: 1990 end-page: 210 ident: br0330 article-title: A study of numerical methods for hyperbolic conservation laws with stiff source terms publication-title: J. Comput. Phys. – year: 1992 ident: br0320 article-title: Numerical Methods for Conservation Laws – year: 2010 ident: br0250 article-title: Detonation shock dynamics calibration for PBX 9502 with temperature, density, and material lot variations publication-title: Fourteenth International Detonation Symposium – start-page: C475 year: 1984 ident: br0540 article-title: Handbook of Chemistry and Physics – volume: 8 start-page: 321 year: 1923 ident: br0170 article-title: Stosswelle und Detonation publication-title: Z. Phys. – volume: 22 start-page: 359 year: 1996 end-page: 379 ident: br0530 article-title: Explicit Runge–Kutta methods for parabolic partial differential equations publication-title: Appl. Numer. Math. – year: 1971 ident: br0450 article-title: The Stefan Problem – volume: 88 start-page: 315 year: 1998 end-page: 326 ident: br0470 article-title: RKC: an explicit solver for parabolic PDEs publication-title: J. Comput. Appl. Math. – volume: ED-32 start-page: 1992 year: 1985 ident: br0130 article-title: Transient simulation of silicon devices and circuits publication-title: IEEE Trans. Electron Devices – year: 1999 ident: br0460 article-title: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry Fluid Mechanics, Computer Vision, and Materials Science, vol. 3 – year: 2006 ident: br0080 article-title: Heat and Mass Transfer – volume: 376 start-page: 1648 year: 2007 end-page: 1658 ident: br0390 article-title: A three-dimensional numerical method for modelling weakly ionized plasmas publication-title: Mon. Not. R. Astron. Soc. – volume: 41 start-page: 455 year: 2000 end-page: 475 ident: br0490 article-title: Fractional step methods applied to a chemotaxis model publication-title: J. Math. Biol. – volume: 39 start-page: 263 year: 2007 end-page: 292 ident: br0160 article-title: The dynamics of detonation in explosive systems publication-title: Annu. Rev. Fluid Mech. – volume: 12 start-page: 31 issue: 1 year: 1996 ident: 10.1016/j.jcp.2013.08.021_br0030 article-title: Super-time-stepping acceleration of explicit schemes for parabolic problems publication-title: Commun. Numer. Methods Eng. doi: 10.1002/(SICI)1099-0887(199601)12:1<31::AID-CNM950>3.0.CO;2-5 – volume: 386 start-page: 627 issue: 2 year: 2008 ident: 10.1016/j.jcp.2013.08.021_br0100 article-title: Simulating anisotropic thermal conduction in supernova remnants—I. Numerical methods publication-title: Mon. Not. R. Astron. Soc. doi: 10.1111/j.1365-2966.2008.13085.x – volume: 224 start-page: 1049 issue: 2 year: 2007 ident: 10.1016/j.jcp.2013.08.021_br0190 article-title: A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.11.004 – volume: 49 start-page: 368 issue: 1 year: 2011 ident: 10.1016/j.jcp.2013.08.021_br0210 article-title: A stability study of a new explicit numerical scheme for a system of differential equations with a large skew-symmetric component publication-title: SIAM J. Numer. Anal. doi: 10.1137/090775804 – year: 2003 ident: 10.1016/j.jcp.2013.08.021_br0240 article-title: The LANL detonation-confinement test: prototype development and sample results – start-page: 475 year: 1975 ident: 10.1016/j.jcp.2013.08.021_br0280 – volume: 86 start-page: 187 issue: 1 year: 1990 ident: 10.1016/j.jcp.2013.08.021_br0330 article-title: A study of numerical methods for hyperbolic conservation laws with stiff source terms publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(90)90097-K – year: 1992 ident: 10.1016/j.jcp.2013.08.021_br0320 – volume: 22 start-page: 359 issue: 1 year: 1996 ident: 10.1016/j.jcp.2013.08.021_br0530 article-title: Explicit Runge–Kutta methods for parabolic partial differential equations publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(96)00022-0 – volume: ED-32 start-page: 1992 year: 1985 ident: 10.1016/j.jcp.2013.08.021_br0130 article-title: Transient simulation of silicon devices and circuits publication-title: IEEE Trans. Electron Devices doi: 10.1109/T-ED.1985.22232 – year: 1971 ident: 10.1016/j.jcp.2013.08.021_br0450 – volume: 151 start-page: 149 issue: 1 year: 2004 ident: 10.1016/j.jcp.2013.08.021_br0090 article-title: Second order accurate schemes for magnetohydrodynamics with divergence-free reconstruction publication-title: Astrophys. J. Suppl. Ser. doi: 10.1086/381377 – volume: 38 start-page: 372 issue: 2 year: 1998 ident: 10.1016/j.jcp.2013.08.021_br0360 article-title: High order explicit methods for parabolic equations publication-title: BIT Numer. Math. doi: 10.1007/BF02512373 – volume: 39 start-page: 263 year: 2007 ident: 10.1016/j.jcp.2013.08.021_br0160 article-title: The dynamics of detonation in explosive systems publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.38.050304.092049 – volume: 29 start-page: 867 issue: 3 year: 1992 ident: 10.1016/j.jcp.2013.08.021_br0440 article-title: A viscosity solutions approach to shape-from-shading publication-title: SIAM J. Numer. Anal. doi: 10.1137/0729053 – volume: 422 start-page: 2102 year: 2012 ident: 10.1016/j.jcp.2013.08.021_br0370 article-title: A second-order accurate Super TimeStepping formulation for anisotropic thermal conduction publication-title: Mon. Not. R. Astron. Soc. doi: 10.1111/j.1365-2966.2012.20744.x – year: 1980 ident: 10.1016/j.jcp.2013.08.021_br0420 – volume: vol. 14 year: 1996 ident: 10.1016/j.jcp.2013.08.021_br0230 article-title: Solving Ordinary Differential Equations II – Stiff and Differential Algebraic Problems – year: 2007 ident: 10.1016/j.jcp.2013.08.021_br0520 – year: 2003 ident: 10.1016/j.jcp.2013.08.021_br0260 – volume: 235 start-page: 934 year: 2013 ident: 10.1016/j.jcp.2013.08.021_br0120 article-title: Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes – comparison with Runge–Kutta methods publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.04.051 – year: 2002 ident: 10.1016/j.jcp.2013.08.021_br0050 article-title: Numerical and theoretical investigations on detonation-inert confinement interactions – volume: 16 start-page: 67 issue: 1 year: 1952 ident: 10.1016/j.jcp.2013.08.021_br0150 article-title: On some unsteady motions of a liquid or a gas in a porous medium publication-title: Prikl. Mat. Meh. – volume: 126 start-page: 390 issue: 2 year: 1996 ident: 10.1016/j.jcp.2013.08.021_br0040 article-title: Level set methods applied to modeling detonation shock dynamics publication-title: J. Comput. Phys. doi: 10.1006/jcph.1996.0145 – volume: 160 start-page: 743 issue: 2 year: 2000 ident: 10.1016/j.jcp.2013.08.021_br0380 article-title: Physics-based preconditioning and the Newton–Krylov method for non-equilibrium radiation diffusion publication-title: J. Comput. Phys. doi: 10.1006/jcph.2000.6488 – volume: 376 start-page: 1648 issue: 4 year: 2007 ident: 10.1016/j.jcp.2013.08.021_br0390 article-title: A three-dimensional numerical method for modelling weakly ionized plasmas publication-title: Mon. Not. R. Astron. Soc. doi: 10.1111/j.1365-2966.2007.11429.x – start-page: C475 year: 1984 ident: 10.1016/j.jcp.2013.08.021_br0540 – year: 2001 ident: 10.1016/j.jcp.2013.08.021_br0010 – volume: 40 start-page: 1729 issue: 12 year: 2000 ident: 10.1016/j.jcp.2013.08.021_br0300 article-title: Explicit difference schemes for solving stiff problems with a complex or separable spectrum publication-title: Comput. Math. Math. Phys. – year: 1964 ident: 10.1016/j.jcp.2013.08.021_br0340 – volume: 228 start-page: 2480 year: 2009 ident: 10.1016/j.jcp.2013.08.021_br0110 article-title: Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2008.12.003 – volume: 5 start-page: 506 issue: 3 year: 1968 ident: 10.1016/j.jcp.2013.08.021_br0480 article-title: On the construction and comparison of difference schemes publication-title: SIAM J. Numer. Anal. doi: 10.1137/0705041 – volume: 80 issue: 1 year: 1997 ident: 10.1016/j.jcp.2013.08.021_br0310 article-title: Ignition phenomena and reaction mechanisms of the self-propagating high-temperature synthesis reaction in the titanium–carbon–aluminum system publication-title: J. Am. Ceram. Soc. doi: 10.1111/j.1151-2916.1997.tb02790.x – volume: vol. 153 year: 2002 ident: 10.1016/j.jcp.2013.08.021_br0400 article-title: Level Set Methods and Dynamic Implicit Surfaces – volume: 3 start-page: 1807 year: 1991 ident: 10.1016/j.jcp.2013.08.021_br0430 article-title: The point explosion with heat conduction publication-title: Phys. Fluids A, Fluid Dyn. doi: 10.1063/1.857961 – volume: 20 start-page: 261 issue: 3 year: 1996 ident: 10.1016/j.jcp.2013.08.021_br0500 article-title: The development of Runge–Kutta methods for partial differential equations publication-title: Appl. Numer. Math. doi: 10.1016/0168-9274(95)00109-3 – volume: 54 start-page: 301 issue: 3 year: 2010 ident: 10.1016/j.jcp.2013.08.021_br0180 article-title: High-order unstructured one-step PNPM schemes for the viscous and resistive MHD equations publication-title: Comput. Model. Eng. Sci. – volume: 23 start-page: 2041 issue: 6 year: 2002 ident: 10.1016/j.jcp.2013.08.021_br0020 article-title: Fourth order Chebyshev methods with recurrence relation publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827500379549 – year: 1990 ident: 10.1016/j.jcp.2013.08.021_br0270 – year: 2006 ident: 10.1016/j.jcp.2013.08.021_br0080 – volume: 34 start-page: 260 issue: 3 year: 2008 ident: 10.1016/j.jcp.2013.08.021_br0200 article-title: A discontinuous Galerkin scheme based on a space–time expansion II. Viscous flow equations in multi dimensions publication-title: J. Sci. Comput. doi: 10.1007/s10915-007-9169-1 – year: 2009 ident: 10.1016/j.jcp.2013.08.021_br0070 article-title: Proton radiography of PBX 9502 detonation shock dynamics sandwich test – year: 1999 ident: 10.1016/j.jcp.2013.08.021_br0460 – volume: 60 start-page: 479 year: 1980 ident: 10.1016/j.jcp.2013.08.021_br0510 article-title: On the internal stability of explicit, m-stage Runge–Kutta methods for large m-values publication-title: Z. Angew. Math. Mech. doi: 10.1002/zamm.19800601005 – year: 2006 ident: 10.1016/j.jcp.2013.08.021_br0060 article-title: Numerical and theoretical investigations on detonation confinement sandwich tests – start-page: 45 year: 1994 ident: 10.1016/j.jcp.2013.08.021_br0290 article-title: How to solve stiff systems of differential equations by explicit methods publication-title: Numer. Methods Appl. – volume: 41 start-page: 455 issue: 5 year: 2000 ident: 10.1016/j.jcp.2013.08.021_br0490 article-title: Fractional step methods applied to a chemotaxis model publication-title: J. Math. Biol. doi: 10.1007/s002850000038 – volume: vol. 1368 start-page: 239 year: 2011 ident: 10.1016/j.jcp.2013.08.021_br0220 article-title: A stability and cost study of explicit and dyadic time stepping for stiff nonsymmetric problems – volume: 88 start-page: 315 issue: 2 year: 1998 ident: 10.1016/j.jcp.2013.08.021_br0470 article-title: RKC: an explicit solver for parabolic PDEs publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(97)00219-7 – volume: 8 start-page: 321 year: 1923 ident: 10.1016/j.jcp.2013.08.021_br0170 article-title: Stosswelle und Detonation publication-title: Z. Phys. doi: 10.1007/BF01329605 – volume: 1 start-page: 24 year: 1958 ident: 10.1016/j.jcp.2013.08.021_br0350 article-title: Effect of radiation on shock wave behavior publication-title: Phys. Fluids (US) doi: 10.1063/1.1724332 – year: 2010 ident: 10.1016/j.jcp.2013.08.021_br0250 article-title: Detonation shock dynamics calibration for PBX 9502 with temperature, density, and material lot variations – volume: 79 start-page: 12 issue: 1 year: 1988 ident: 10.1016/j.jcp.2013.08.021_br0410 article-title: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(88)90002-2 |
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| Title | A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations |
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