Third-Order Inviscid and Second-Order Hyperbolic Navier-Stokes Solvers for Three-Dimensional Unsteady Inviscid and Viscous Flows

This paper presents third-order-inviscid implicit edge-based solvers for unsteady inviscid and viscous flows on unstructured tetrahedral grids. Steady third-order-inviscid solvers recently developed in NASA’s FUN3D code are extended to unsteady computations with implicit time-stepping schemes. The physical time derivative is discretized by a backward-difference formula, and incorporated into the third-order edge-base scheme as a source term. In the third-order edge-based scheme, the source term needs to be discretized in space by a special formula to preserve third-order accuracy. A very economical source discretization formula is derived, and the resulting unsteady third-order unstructured-grid scheme is made completely free from second derivative computations. Developed unsteady schemes are investigated and compared for some representative test cases for unsteady inviscid and viscous flows.

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