A posteriori error analysis for a cut cell finite volume method

Journal Article · Thu Sep 01 04:00:00 EDT 2011 · Computer Methods in Applied Mechanics and Engineering

OSTI ID:1018731

Wang, Haiying; Pernice, Michael; Tavener, Simon; Estep, Don

We study the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. We consider discretizations that use regularly-shaped meshes, so that the interface “cuts” through the cells (elements or volumes) without respecting the regular geometry of the mesh. Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. This motivates the derivation of computational error estimates that yield accurate estimates for specified quantities of interest. For this purpose, we adapt the well-known adjoint based a posteriori error analysis technique used for finite element methods. In order to employ this method, we describe a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1018731
• Report Number(s): INL/JOU-09-17376
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: 37 - 40 Vol. 200; ISSN 0045-7825; ISSN CMMECC
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ACCURACY
CONVERGENCE
DIFFUSION
FINITE ELEMENT METHOD
GEOMETRY
a posteriori error analysis
cut cell discretization
discontinuous diffusion coefficient