Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 6, Issue 3, Pages 28-56Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/20116302
Keywords
high-order; mixed unstructured grids; Navier-Stokes equations; discontinuous Galerkin; spectral collocation; finite difference
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Funding
- Air Force Office of Scientific Research (AFOSR) [FA9550-09-1-0128]
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The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be completely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compressible Navier-Stokes equations to demonstrate its performance.
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