Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving the steady Navier–Stokes equations

The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower–uppe...

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Vydané v:	Journal of computational physics Ročník 229; číslo 3; s. 828 - 850
Hlavní autori:	Parsani, M., Van den Abeele, K., Lacor, C., Turkel, E.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier Inc 01.02.2010 Elsevier
Predmet:	Algorithms Boundary element method Computational techniques Cylinders Exact sciences and technology High-order methods Implicit LU-SGS algorithm Laminar Mach number Mathematical analysis Mathematical methods in physics Navier-Stokes equations Navier–Stokes p-Multigrid Physics Runge-Kutta method Von Neumann analysis Navier–Stokes p-Multigrid High-order methods Implicit LU-SGS algorithm Von Neumann analysis Damping Spectral method Fluid dynamics Aspect ratio Euler scheme Calculation methods Advection Algorithms Laminar flow Multigrid Convergence rate Navier-Stokes Calculation Cylinders Navier-Stokes equations Mach number
ISSN:	0021-9991, 1090-2716
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Abstract	The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. The implicit method addresses the stiffness in the discrete Navier–Stokes equations associated with stretched meshes. The LU-SGS algorithm is then used as a smoother for a p-multigrid approach. A Von Neumann stability analysis is applied to the two-dimensional linear advection equation to determine its damping properties. The implicit LU-SGS scheme is used to solve the two-dimensional (2D) compressible laminar Navier–Stokes equations. We compute the solution of a laminar external flow over a cylinder and around an airfoil at low Mach number. We compare the convergence rates with explicit Runge–Kutta (E-RK) schemes employed as a smoother. The effects of the cell aspect ratio and the low Mach number on the convergence are investigated. With the p-multigrid method and the implicit smoother the computational time can be reduced by a factor of up to 5–10 compared with a well tuned E-RK scheme.
AbstractList	The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm. The implicit method addresses the stiffness in the discrete Navier-Stokes equations associated with stretched meshes. The LU-SGS algorithm is then used as a smoother for a p-multigrid approach. A von Neumann stability analysis is applied to the two-dimensional linear advection equation to determine its damping properties. The implicit LU-SGS scheme is used to solve the two-dimensional (2D) compressible laminar Navier-Stokes equations. We compute the solution of a laminar external flow over a cylinder and around an airfoil at low Mach number. We compare the convergence rates with explicit Runge-Kutta (E-RK) schemes employed as a smoother. The effects of the cell aspect ratio and the low Mach number on the convergence are investigated. With the p-multigrid method and the implicit smoother the computational time can be reduced by a factor of up to 5-10 compared with a well tuned E-RK scheme. The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. The implicit method addresses the stiffness in the discrete Navier–Stokes equations associated with stretched meshes. The LU-SGS algorithm is then used as a smoother for a p-multigrid approach. A Von Neumann stability analysis is applied to the two-dimensional linear advection equation to determine its damping properties. The implicit LU-SGS scheme is used to solve the two-dimensional (2D) compressible laminar Navier–Stokes equations. We compute the solution of a laminar external flow over a cylinder and around an airfoil at low Mach number. We compare the convergence rates with explicit Runge–Kutta (E-RK) schemes employed as a smoother. The effects of the cell aspect ratio and the low Mach number on the convergence are investigated. With the p-multigrid method and the implicit smoother the computational time can be reduced by a factor of up to 5–10 compared with a well tuned E-RK scheme.
Author	Lacor, C. Van den Abeele, K. Parsani, M. Turkel, E.
Author_xml	– sequence: 1 givenname: M. surname: Parsani fullname: Parsani, M. email: mparsani@vub.ac.be organization: Vrije Universiteit Brussel, Department of Mechanical Engineering, Fluid Dynamics and Thermodynamics Research Group, Pleinlaan 2, 1050 Brussel, Belgium – sequence: 2 givenname: K. surname: Van den Abeele fullname: Van den Abeele, K. email: kvdabeel@vub.ac.be organization: Vrije Universiteit Brussel, Department of Mechanical Engineering, Fluid Dynamics and Thermodynamics Research Group, Pleinlaan 2, 1050 Brussel, Belgium – sequence: 3 givenname: C. surname: Lacor fullname: Lacor, C. email: chris.lacor@vub.ac.be organization: Vrije Universiteit Brussel, Department of Mechanical Engineering, Fluid Dynamics and Thermodynamics Research Group, Pleinlaan 2, 1050 Brussel, Belgium – sequence: 4 givenname: E. surname: Turkel fullname: Turkel, E. email: turkel@post.tau.ac.il organization: Tel-Aviv University, Department of Mathematics, Tel-Aviv, Ramat Aviv 69978, Israel
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Keywords	Navier–Stokes p-Multigrid High-order methods Implicit LU-SGS algorithm Von Neumann analysis Damping Spectral method Fluid dynamics Aspect ratio Euler scheme Calculation methods Advection Algorithms Laminar flow Multigrid Convergence rate Navier-Stokes Calculation Cylinders Navier-Stokes equations Mach number
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References	Cockburn, Shu (bib1) 1989; 52 Jameson, Turkel (bib22) 1981; 37 Cockburn, Lin, Shu (bib2) 1989; 84 Ricchiuto, Csík, Deconinck (bib6) 2005; 209 Liu, Vinokur, Wang (bib11) 2006; 212 Helenbrook, Atkins (bib31) 2005; 44 Lax (bib28) 1954; VII Barlow, Rae, Pope (bib34) 1999 Wang, Zhang, Liu (bib10) 2004; 194 Cockburn, Hou, Shu (bib3) 1990; 54 Sun, Wang, Liu (bib12) 2006; 215 Wang, Liu (bib13) 2006; 211 G. May, A. Jameson, A spectral difference method for the Euler and Navier–Stokes equations on unstructured meshes, in: 44th AIAA Aerospace Sciences Meeting Reno, Nevada, January 2006. M. Parsani, K. Van den Abeele, C. Lacor, Implicit LU-SGS time integration algorithm for high-order spectral volume method with Brandt (bib16) 1982 Wang, Liu (bib9) 2004; 20 Roe (bib29) 1981; 43 H. Bijl, M.H. Carpenter, V.N. Vatsa, Time integration schemes for the unsteady Navier–Stokes equations, AIAA Paper 2001–2612, 2001. Liu, Vinokur, Wang (bib17) 2006; 216 Buelow, Venkateswaran, Merkle (bib25) 2001; 30 Geuzaine, Remacle (bib33) 2009; 79 Cockburn, Shu (bib4) 1998; 141 Y. Sun, Z.J. Wang, Y. Liu, C.-L. Chen, Efficient implicit LU-SGS algorithm for high-order spectral difference method on unstructured hexahedral grids, in: 45th AIAA Aerospace Sciences Meeting, Reno, Nevada, January 2007. Swanson, Turkel, Rossow (bib21) 2007; 224 Van den Abeele, Lacor (bib15) 2007; 226 multigrid strategy, in: West-East High-Speed Flow Field Conference, Moscow, Russia, November 2007. Experimental data base for computer program assessment, AGARD AR-138, May, 1979. Quarteroni, Sacco, Saleri (bib30) 2002 Van den Abeele, Broeckhoven, Lacor (bib14) 2006; 224 Cockburn, Shu (bib5) 1998; 35 Wang (bib7) 2002; 178 Jameson, Yoon (bib23) 1987; 25 Wang, Liu (bib8) 2002; 179 Kim, Kwon (bib26) 2007; 36 Sharov, Nakahashi (bib32) 1998; 36 Wang, Liu, May, Jameson (bib19) 2007; 32 Swanson (10.1016/j.jcp.2009.10.014_bib21) 2007; 224 Helenbrook (10.1016/j.jcp.2009.10.014_bib31) 2005; 44 Cockburn (10.1016/j.jcp.2009.10.014_bib4) 1998; 141 Cockburn (10.1016/j.jcp.2009.10.014_bib5) 1998; 35 Van den Abeele (10.1016/j.jcp.2009.10.014_bib15) 2007; 226 Brandt (10.1016/j.jcp.2009.10.014_bib16) 1982 Ricchiuto (10.1016/j.jcp.2009.10.014_bib6) 2005; 209 Geuzaine (10.1016/j.jcp.2009.10.014_bib33) 2009; 79 Barlow (10.1016/j.jcp.2009.10.014_bib34) 1999 Lax (10.1016/j.jcp.2009.10.014_bib28) 1954; VII Liu (10.1016/j.jcp.2009.10.014_bib17) 2006; 216 10.1016/j.jcp.2009.10.014_bib35 10.1016/j.jcp.2009.10.014_bib18 Jameson (10.1016/j.jcp.2009.10.014_bib23) 1987; 25 Quarteroni (10.1016/j.jcp.2009.10.014_bib30) 2002 Cockburn (10.1016/j.jcp.2009.10.014_bib3) 1990; 54 Wang (10.1016/j.jcp.2009.10.014_bib13) 2006; 211 Liu (10.1016/j.jcp.2009.10.014_bib11) 2006; 212 Wang (10.1016/j.jcp.2009.10.014_bib7) 2002; 178 10.1016/j.jcp.2009.10.014_bib20 Jameson (10.1016/j.jcp.2009.10.014_bib22) 1981; 37 10.1016/j.jcp.2009.10.014_bib24 Cockburn (10.1016/j.jcp.2009.10.014_bib2) 1989; 84 Buelow (10.1016/j.jcp.2009.10.014_bib25) 2001; 30 10.1016/j.jcp.2009.10.014_bib27 Wang (10.1016/j.jcp.2009.10.014_bib19) 2007; 32 Cockburn (10.1016/j.jcp.2009.10.014_bib1) 1989; 52 Sun (10.1016/j.jcp.2009.10.014_bib12) 2006; 215 Roe (10.1016/j.jcp.2009.10.014_bib29) 1981; 43 Van den Abeele (10.1016/j.jcp.2009.10.014_bib14) 2006; 224 Wang (10.1016/j.jcp.2009.10.014_bib10) 2004; 194 Kim (10.1016/j.jcp.2009.10.014_bib26) 2007; 36 Wang (10.1016/j.jcp.2009.10.014_bib8) 2002; 179 Sharov (10.1016/j.jcp.2009.10.014_bib32) 1998; 36 Wang (10.1016/j.jcp.2009.10.014_bib9) 2004; 20
References_xml	– volume: 35 start-page: 2440 year: 1998 end-page: 2463 ident: bib5 article-title: The local discontinuous Galerkin method for time-dependent convection–diffusion systems publication-title: SIAM Journal of Numerical Analysis – reference: H. Bijl, M.H. Carpenter, V.N. Vatsa, Time integration schemes for the unsteady Navier–Stokes equations, AIAA Paper 2001–2612, 2001. – volume: 178 start-page: 210 year: 2002 end-page: 251 ident: bib7 article-title: Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation publication-title: Journal of Computational Physics – volume: 179 start-page: 665 year: 2002 end-page: 697 ident: bib8 article-title: Spectral (finite) volume method for conservation laws on unstructured grids II: extension to two-dimensional scalar equation publication-title: Journal of Computational Physics – reference: M. Parsani, K. Van den Abeele, C. Lacor, Implicit LU-SGS time integration algorithm for high-order spectral volume method with – volume: 54 start-page: 545 year: 1990 end-page: 581 ident: bib3 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case publication-title: Mathematics of Computation – reference: Y. Sun, Z.J. Wang, Y. Liu, C.-L. Chen, Efficient implicit LU-SGS algorithm for high-order spectral difference method on unstructured hexahedral grids, in: 45th AIAA Aerospace Sciences Meeting, Reno, Nevada, January 2007. – volume: 224 start-page: 365 year: 2007 end-page: 388 ident: bib21 article-title: Convergence acceleration of Runge–Kutta schemes for solving the Navier–Stokes equations publication-title: Journal of Computational Physics – reference: G. May, A. Jameson, A spectral difference method for the Euler and Navier–Stokes equations on unstructured meshes, in: 44th AIAA Aerospace Sciences Meeting Reno, Nevada, January 2006. – volume: 224 start-page: 616 year: 2006 end-page: 636 ident: bib14 article-title: Dispersion and dissipation properties of the 1D spectral volume method and application to a publication-title: Journal of Computational Physics – volume: 226 start-page: 1007 year: 2007 end-page: 10026 ident: bib15 article-title: An accuracy and stability study of the 2D spectral volume method publication-title: Journal of Computational Physics – volume: 20 start-page: 137 year: 2004 end-page: 157 ident: bib9 article-title: Spectral (finite) volume method for conservation laws on unstructured grids III: one-dimensional systems and partition optimization publication-title: Journal of Scientific Computing – volume: 36 start-page: 1335 year: 2007 end-page: 1346 ident: bib26 article-title: Assessment of implicit operators for the upwind point Gauss–Seidel method on unstructured meshes publication-title: Computer and Fluids – volume: 52 start-page: 411 year: 1989 end-page: 435 ident: bib1 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework publication-title: Mathematics of Computation – volume: 212 start-page: 454 year: 2006 end-page: 472 ident: bib11 article-title: Spectral (finite) volume method for conservation laws on unstructured grids V: extension to three-dimensional systems publication-title: Journal of Computational Physics – volume: 194 start-page: 716 year: 2004 end-page: 741 ident: bib10 article-title: Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional Euler equations publication-title: Journal of Computational Physics – volume: 141 start-page: 199 year: 1998 end-page: 224 ident: bib4 article-title: The Runge–Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems publication-title: Journal of Computational Physics – volume: 215 start-page: 41 year: 2006 end-page: 58 ident: bib12 article-title: Spectral (finite) volume method for conservation laws on unstructured grids VI: extension to viscous flow publication-title: Journal of Computational Physics – year: 1999 ident: bib34 article-title: Low-Speed Wind Tunnel Testing – year: 2002 ident: bib30 article-title: Numerical Mathematics – volume: 209 start-page: 249 year: 2005 end-page: 289 ident: bib6 article-title: Residual distribution for general time-dependent conservation laws publication-title: Journal of Computational Physics – volume: VII start-page: 159 year: 1954 end-page: 193 ident: bib28 article-title: Weak solutions of non-linear hyperbolic equations and their numerical computation publication-title: Communications on Pure and Applied Mathematics – reference: Experimental data base for computer program assessment, AGARD AR-138, May, 1979. – year: 1982 ident: bib16 article-title: Guide to Multigrid Development – volume: 32 start-page: 449 year: 2007 end-page: 454 ident: bib19 article-title: Spectral difference method for unstructured grids II: extension to the Euler equations publication-title: Journal of Scientific Computing – volume: 44 start-page: 566 year: 2005 end-page: 575 ident: bib31 article-title: Application of publication-title: AIAA Journal – volume: 30 start-page: 961 year: 2001 end-page: 988 ident: bib25 article-title: Stability and convergence analysis of implicit upwind schemes publication-title: Computer and Fluids – volume: 211 start-page: 154 year: 2006 end-page: 178 ident: bib13 article-title: Extension of the spectral volume method to high-order boundary representation publication-title: Journal of Computational Physics – volume: 37 start-page: 385 year: 1981 end-page: 397 ident: bib22 article-title: Implicit schemes and LU decompositions publication-title: Mathematics of Computations – volume: 84 start-page: 90 year: 1989 end-page: 113 ident: bib2 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems publication-title: Journal of Computational Physics – reference: -multigrid strategy, in: West-East High-Speed Flow Field Conference, Moscow, Russia, November 2007. – volume: 36 start-page: 484 year: 1998 end-page: 486 ident: bib32 article-title: Reordering of hybrid unstructured grids for lower–upper symmetric Gauss–Seidel computations publication-title: AIAA Journal – volume: 25 start-page: 929 year: 1987 end-page: 935 ident: bib23 article-title: Lower–upper implicit schemes with multiple grids for the Euler equations publication-title: AIAA Journal – volume: 43 start-page: 357 year: 1981 end-page: 372 ident: bib29 article-title: Approximate Riemann solvers parameter vectors and difference scheme publication-title: Journal of Computational Physics – volume: 216 start-page: 780 year: 2006 end-page: 801 ident: bib17 article-title: Spectral difference method for unstructured grids I: basic formulation publication-title: Journal of Computational Physics – volume: 79 start-page: 1309 year: 2009 end-page: 1331 ident: bib33 article-title: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities publication-title: International Journal for Numerical Methods in Engineering – volume: 226 start-page: 1007 year: 2007 ident: 10.1016/j.jcp.2009.10.014_bib15 article-title: An accuracy and stability study of the 2D spectral volume method publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2007.05.004 – volume: 211 start-page: 154 year: 2006 ident: 10.1016/j.jcp.2009.10.014_bib13 article-title: Extension of the spectral volume method to high-order boundary representation publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2005.05.022 – volume: 194 start-page: 716 issue: 2 year: 2004 ident: 10.1016/j.jcp.2009.10.014_bib10 article-title: Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional Euler equations publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2003.09.012 – volume: 35 start-page: 2440 issue: 6 year: 1998 ident: 10.1016/j.jcp.2009.10.014_bib5 article-title: The local discontinuous Galerkin method for time-dependent convection–diffusion systems publication-title: SIAM Journal of Numerical Analysis doi: 10.1137/S0036142997316712 – ident: 10.1016/j.jcp.2009.10.014_bib24 doi: 10.2514/6.2007-313 – volume: 36 start-page: 484 issue: 3 year: 1998 ident: 10.1016/j.jcp.2009.10.014_bib32 article-title: Reordering of hybrid unstructured grids for lower–upper symmetric Gauss–Seidel computations publication-title: AIAA Journal doi: 10.2514/2.392 – volume: 79 start-page: 1309 issue: 11 year: 2009 ident: 10.1016/j.jcp.2009.10.014_bib33 article-title: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.2579 – volume: 224 start-page: 616 issue: 2 year: 2006 ident: 10.1016/j.jcp.2009.10.014_bib14 article-title: Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2006.10.022 – volume: 52 start-page: 411 year: 1989 ident: 10.1016/j.jcp.2009.10.014_bib1 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework publication-title: Mathematics of Computation – volume: 30 start-page: 961 year: 2001 ident: 10.1016/j.jcp.2009.10.014_bib25 article-title: Stability and convergence analysis of implicit upwind schemes publication-title: Computer and Fluids doi: 10.1016/S0045-7930(01)00038-X – volume: 212 start-page: 454 year: 2006 ident: 10.1016/j.jcp.2009.10.014_bib11 article-title: Spectral (finite) volume method for conservation laws on unstructured grids V: extension to three-dimensional systems publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2005.06.024 – volume: VII start-page: 159 year: 1954 ident: 10.1016/j.jcp.2009.10.014_bib28 article-title: Weak solutions of non-linear hyperbolic equations and their numerical computation publication-title: Communications on Pure and Applied Mathematics doi: 10.1002/cpa.3160070112 – volume: 179 start-page: 665 year: 2002 ident: 10.1016/j.jcp.2009.10.014_bib8 article-title: Spectral (finite) volume method for conservation laws on unstructured grids II: extension to two-dimensional scalar equation publication-title: Journal of Computational Physics doi: 10.1006/jcph.2002.7082 – volume: 32 start-page: 449 issue: 1 year: 2007 ident: 10.1016/j.jcp.2009.10.014_bib19 article-title: Spectral difference method for unstructured grids II: extension to the Euler equations publication-title: Journal of Scientific Computing doi: 10.1007/s10915-006-9113-9 – volume: 141 start-page: 199 year: 1998 ident: 10.1016/j.jcp.2009.10.014_bib4 article-title: The Runge–Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems publication-title: Journal of Computational Physics doi: 10.1006/jcph.1998.5892 – volume: 43 start-page: 357 year: 1981 ident: 10.1016/j.jcp.2009.10.014_bib29 article-title: Approximate Riemann solvers parameter vectors and difference scheme publication-title: Journal of Computational Physics doi: 10.1016/0021-9991(81)90128-5 – volume: 84 start-page: 90 year: 1989 ident: 10.1016/j.jcp.2009.10.014_bib2 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems publication-title: Journal of Computational Physics doi: 10.1016/0021-9991(89)90183-6 – year: 1982 ident: 10.1016/j.jcp.2009.10.014_bib16 – volume: 54 start-page: 545 year: 1990 ident: 10.1016/j.jcp.2009.10.014_bib3 article-title: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case publication-title: Mathematics of Computation – year: 2002 ident: 10.1016/j.jcp.2009.10.014_bib30 – volume: 20 start-page: 137 year: 2004 ident: 10.1016/j.jcp.2009.10.014_bib9 article-title: Spectral (finite) volume method for conservation laws on unstructured grids III: one-dimensional systems and partition optimization publication-title: Journal of Scientific Computing doi: 10.1023/A:1025896119548 – volume: 37 start-page: 385 year: 1981 ident: 10.1016/j.jcp.2009.10.014_bib22 article-title: Implicit schemes and LU decompositions publication-title: Mathematics of Computations – volume: 224 start-page: 365 year: 2007 ident: 10.1016/j.jcp.2009.10.014_bib21 article-title: Convergence acceleration of Runge–Kutta schemes for solving the Navier–Stokes equations publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2007.02.028 – volume: 44 start-page: 566 issue: 3 year: 2005 ident: 10.1016/j.jcp.2009.10.014_bib31 article-title: Application of p-multigrid to discontinuous Galerkin formulations of the Poisson equation publication-title: AIAA Journal doi: 10.2514/1.15497 – ident: 10.1016/j.jcp.2009.10.014_bib27 – volume: 36 start-page: 1335 year: 2007 ident: 10.1016/j.jcp.2009.10.014_bib26 article-title: Assessment of implicit operators for the upwind point Gauss–Seidel method on unstructured meshes publication-title: Computer and Fluids doi: 10.1016/j.compfluid.2006.12.009 – ident: 10.1016/j.jcp.2009.10.014_bib20 doi: 10.2514/6.2001-2612 – volume: 209 start-page: 249 year: 2005 ident: 10.1016/j.jcp.2009.10.014_bib6 article-title: Residual distribution for general time-dependent conservation laws publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2005.03.003 – volume: 25 start-page: 929 issue: 7 year: 1987 ident: 10.1016/j.jcp.2009.10.014_bib23 article-title: Lower–upper implicit schemes with multiple grids for the Euler equations publication-title: AIAA Journal doi: 10.2514/3.9724 – year: 1999 ident: 10.1016/j.jcp.2009.10.014_bib34 – ident: 10.1016/j.jcp.2009.10.014_bib35 – volume: 216 start-page: 780 year: 2006 ident: 10.1016/j.jcp.2009.10.014_bib17 article-title: Spectral difference method for unstructured grids I: basic formulation publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2006.01.024 – volume: 178 start-page: 210 year: 2002 ident: 10.1016/j.jcp.2009.10.014_bib7 article-title: Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation publication-title: Journal of Computational Physics doi: 10.1006/jcph.2002.7041 – volume: 215 start-page: 41 year: 2006 ident: 10.1016/j.jcp.2009.10.014_bib12 article-title: Spectral (finite) volume method for conservation laws on unstructured grids VI: extension to viscous flow publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2005.10.019 – ident: 10.1016/j.jcp.2009.10.014_bib18 doi: 10.2514/6.2006-304
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Snippet	The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations...
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SubjectTerms	Algorithms Boundary element method Computational techniques Cylinders Exact sciences and technology High-order methods Implicit LU-SGS algorithm Laminar Mach number Mathematical analysis Mathematical methods in physics Navier-Stokes equations Navier–Stokes p-Multigrid Physics Runge-Kutta method Von Neumann analysis
Title	Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving the steady Navier–Stokes equations
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