An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation. Issue 12 (20th August 2021)

• Record Type: Journal Article
• Authors: Para, Kanokwarun; Jitsom, Bubpha; Eymard, Robert; Sungnul, Surattana; Sirisubtawee, Sekson; Phongthanapanich, Sutthisak
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 101:Issue 12(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-08-20
• Subjects: characteristic finite volume method -- convection‐diffusion equation -- piecewise linear reconstruction -- two‐dimensional triangular grid; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201900245
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L 2 norm of the error is derived to determine the errors for the approximate solution. The accuracy of four piecewise linear reconstruction techniques, namely, Frink, Holmes‐Connell, Green‐Gauss, and least‐squares methods are investigated on structured triangular grids. Numerical evidence shows that the least‐squares method is the most accurate of all methods for smooth initial condition problems. For discontinuous initial condition problems, the Frink and the Holmes‐Connell methods give a spurious oscillating solution in the vicinity of the discontinuity upstream of the discontinuity, and the Green‐Gauss and least‐squares methods give a spurious oscillating solution in the vicinity of the discontinuity downstream of the discontinuity. Moreover, the amplitude of the oscillation could be amplified on the finer grid sizes. Abstract : In this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L 2 norm of the error is derived to determine the errors for the approximate solution.…