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A Comparative Study of Compact Finite Volume Methods for the 2-D Difussion Equation with Finite Difference ADI and SOR

B.N. Borah, R.E. White, A.J. Kyrillidis, S. Sankarlingham

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Abstract

Recently developed Compact Finite Difference scheme (CPT) is applied to two dimensional diffusion equations. The relative merits of CPT-ADI are investigated with other computational schemes such as finite difference method ADI (FDM-ADI) and FDM-SOR. The numerical results obtained from these three approaches are compared to known analytical solutions. The primary interest of this study lies on vectorization and parallel processing. According to our results shown in tables 1 CPT-ADI is found to be superior scheme with regards to accuracy, than both FDM-ADI and FDM-SOR. It is also fastest algorithm than both FDM-ADI and FDM-SOR as it is evident from CPU times.

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What this paper is about

Recently developed Compact Finite Difference scheme (CPT) is applied to two dimensional diffusion equations. The relative merits of CPT-ADI are investigated with other computational schemes such as finite difference method ADI (FDM-ADI) and FDM-SOR. The numerical results obtained from these three approaches are compared to known analytical solutions. The primary interest of this study lies on vectorization and parallel processing. According to our results shown in tables 1 CPT-ADI is found to be superior scheme with regards to accuracy, than both FDM-ADI and FDM-SOR. It is also fastest algorithm than both FDM-ADI and FDM-SOR as it is evident from CPU times.

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Available abstract

Recently developed Compact Finite Difference scheme (CPT) is applied to two dimensional diffusion equations. The relative merits of CPT-ADI are investigated with other computational schemes such as finite difference method ADI (FDM-ADI) and FDM-SOR. The numerical results obtained from these three approaches are compared to known analytical solutions. The primary interest of this study lies on vectorization and parallel processing. According to our results shown in tables 1 CPT-ADI is found to be superior scheme with regards to accuracy, than both FDM-ADI and FDM-SOR. It is also fastest algorithm than both FDM-ADI and FDM-SOR as it is evident from CPU times.

Key concepts: Alternating direction implicit method, Finite difference method, Finite difference coefficient, Finite volume method, Mathematics, Finite difference, Vectorization (mathematics), Finite volume method for one-dimensional steady state diffusion

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A Comparative Study of Compact Finite Volume Methods for the 2-D Difussion Equation with Finite Difference ADI and SOR — Research Paper | ScholarLens