Higher-order time integration schemes for the unsteady Navier–Stokes equations on unstructured meshes
The efficiency gains obtained using higher-order implicit Runge–Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier–Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at eac...
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| Vydané v: | Journal of computational physics Ročník 191; číslo 2; s. 542 - 566 |
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| Jazyk: | English |
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01.11.2003
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| Abstract | The efficiency gains obtained using higher-order implicit Runge–Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier–Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each time step are presented. The first algorithm (nonlinear multigrid, NMG) is a pseudo-time-stepping scheme which employs a nonlinear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on inexact Newton’s methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson’s iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the generalized minimal residual method. Results demonstrating the relative superiority of these Newton’s method based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes such as fourth-order Runge–Kutta (RK64) with the more efficient inexact Newton’s method based schemes (LMG). |
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| AbstractList | The efficiency gains obtained using higher-order implicit Runge–Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier–Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each time step are presented. The first algorithm (nonlinear multigrid, NMG) is a pseudo-time-stepping scheme which employs a nonlinear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on inexact Newton’s methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson’s iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the generalized minimal residual method. Results demonstrating the relative superiority of these Newton’s method based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes such as fourth-order Runge–Kutta (RK64) with the more efficient inexact Newton’s method based schemes (LMG). The efficiency gains obtained using higher-order implicit Runge-Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each time step are presented. The first algorithm (nonlinear multigrid, NMG) is a pseudo- time-stepping scheme which employs a nonlinear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the generalized minimal residual method. Results demonstrating the relative superiority of these Newton's method based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes such as fourth- order Runge-Kutta (RK64) with the more efficient inexact Newton's method based schemes (LMG). (Author) |
| Author | Mavriplis, Dimitri J. Caughey, David A. Jothiprasad, Giridhar |
| Author_xml | – sequence: 1 givenname: Giridhar surname: Jothiprasad fullname: Jothiprasad, Giridhar email: gj24@cornell.edu organization: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA – sequence: 2 givenname: Dimitri J. surname: Mavriplis fullname: Mavriplis, Dimitri J. email: dimitri@icase.edu organization: National Institute of Aerospace, 144 Research Drive, Hampton, VA 23666, USA – sequence: 3 givenname: David A. surname: Caughey fullname: Caughey, David A. email: dac5@cornell.edu organization: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA |
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| Cites_doi | 10.1080/10407788608913491 10.2514/6.1985-1494 10.1137/0719025 10.1006/jcph.2001.6948 10.1007/BF01963532 10.1017/S0022112097007465 10.2514/2.590 10.1006/jcph.1998.6036 10.2514/6.1997-2025 10.1006/jcph.2000.6488 10.1006/jfls.1998.0184 10.1137/0907058 10.2514/6.2001-2612 10.2514/6.1998-2966 |
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