Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes
Veluri, Subrahmanya Pavan Kumar
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A detailed code verification study of an unstructured finite volume Computational Fluid Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to generate exact solutions for the Euler and Navier-Stokes equations to verify the correctness of the code through order of accuracy testing. The verification testing is performed on different mesh types which include triangular and quadrilateral elements in 2D and tetrahedral, prismatic, and hexahedral elements in 3D. The requirements of systematic mesh refinement are discussed, particularly in regards to unstructured meshes. Different code options verified include the baseline steady state governing equations, transport models, turbulence models, boundary conditions and unsteady flows. Coding mistakes, algorithm inconsistencies, and mesh quality sensitivities uncovered during the code verification are presented. In recent years, there has been significant work on the development of algorithms for the compressible Navier-Stokes equations on unstructured grids. One of the challenging tasks during the development of these algorithms is the formulation of consistent and accurate diffusion operators. The robustness and accuracy of diffusion operators depends on mesh quality. A survey of diffusion operators for compressible CFD solvers is conducted to understand different formulation procedures for diffusion fluxes. A patch-wise version of the Method of Manufactured Solutions is used to test the accuracy of selected diffusion operators. This testing of diffusion operators is limited to cell-centered finite volume methods which are formally second order accurate. These diffusion operators are tested and compared on different 2D mesh topologies to study the effect of mesh quality (stretching, aspect ratio, skewness, and curvature) on their numerical accuracy. Quantities examined include the numerical approximation errors and order of accuracy associated with face gradient reconstruction. From the analysis, defects in some of the numerical formulations are identified along with some robust and accurate diffusion operators.
- Doctoral Dissertations