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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Shrnutí: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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.10.014