Title page for ETD etd-08182010-155814

Type of Document Dissertation
Author Veluri, Subrahmanya Pavan Kumar
Author's Email Address veluris@vt.edu
URN etd-08182010-155814
Title Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Roy, Christopher J. Committee Chair
Mason, William H. Committee Member
McCue-Weil, Leigh S. Committee Member
Tafti, Danesh K. Committee Member
  • Order of Accuracy
  • Computational Fluid Dynamics
  • Discretization Error
  • Method of Manufactured Solutions
  • Code Verification
Date of Defense 2010-08-06
Availability unrestricted
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


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