An efficient finite volume TVD scheme for steady-state solutions of the 3-D compressible Euler/Navier-Stokes equations
Abstract
The formulation and validation of an efficient spatially second-order accurate finite volume total variation diminishing (TVD) scheme in general curvilinear coordinates for the 3-D compressible Navier-Stokes equations in strong conservation law form is presented. Approximate factorization and flux splitting are not utilized; therefore the associated extra, unwanted numerical dissipation is avoided, especially in complex viscous problems. A general line relaxation procedure is used to accelerate the convergence rate for geometrically complex steady-state problems since it is completely vectorizable. The implicit operator is cast in a delta-form using a TVD preconditioning matrix. The explicit part is evaluated using the same finite-volume TVD procedures developed by the authors in previous publications. This procedure preserves the high-resolution TVD characteristics in the steady state even at high CFL numbers. Numerical results are presented which demonstrate the efficiency, accuracy, and convergence characteristics for single and multi-body inviscid and turbulent flows.
- Publication:
-
AIAA, Fluid Dynamics, 21st Plasma Dynamics and Lasers Conference, 21st, Seattle, WA, June 18-20, 1990. 17 p.
- Pub Date:
- June 1990
- Bibcode:
- 1990fdpd.confS....W
- Keywords:
-
- Compressible Flow;
- Computational Fluid Dynamics;
- Euler Equations Of Motion;
- Finite Volume Method;
- Navier-Stokes Equation;
- Steady State;
- Three Dimensional Flow;
- Tvd Schemes;
- Algorithms;
- Conservation Laws;
- Inviscid Flow;
- Spherical Coordinates;
- Turbulent Flow;
- Fluid Mechanics and Heat Transfer