Verification of a three-dimensional unstructured finite element method using analytic and manufactured solutions

Autor: John G. Wohlbier, Nathaniel R. Morgan, L. D. Risinger, Thomas R. Canfield, Jacob Waltz
Rok vydání: 2013
Předmět:
Zdroj: Computers & Fluids. 81:57-67
ISSN: 0045-7930
DOI: 10.1016/j.compfluid.2013.03.025
Popis: We report on the verification of a three-dimensional unstructured finite element method applicable to compressible fluid dynamics and diffusion problems. Our verification methodology uses a combination of analytic and manufactured solutions to formally measure convergence rates in global error for both shock-dominated flows and smooth problems. In addition we measure the global error in vorticity, which should converge at reduced-order relative to the velocity solution. The numerical method under investigation is an edge-based Finite Element formulation on linear tetrahedra with a parabolic MUSCL reconstruction for the advective fluxes. The scheme is nominally second-order accurate on smooth flows. For diffusion problems the formulation also is nominally second-order accurate. Using global error analysis we measure convergence rates of 0.8–1.0 for shock-dominated problems and 1.5–2.4 for smooth problems. Calculations with Adaptive Mesh Refinement (AMR) are observed to produce errors comparable to finer mesh simulations but at significantly reduced computational cost. A convergence rate of 2.2 also is observed for a simplified diffusion problem. Examples of how these studies can inform simulation practices are provided.
Databáze: OpenAIRE
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