A new positive finite volume scheme for two‐dimensional convection‐diffusion equation. Issue 2 (5th November 2018)

• Record Type: Journal Article
• Authors: Lan, Bin; Sheng, Zhiqiang; Yuan, Guangwei
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 99:Issue 2(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-11-05
• Subjects: convection‐diffusion equation -- deformed meshes -- nonlinear -- positivity; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800067
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: A new positive finite volume scheme for the two‐dimensional convection‐diffusion equation on deformed meshes is proposed. The approximation of the convective flux is based on some available information of the diffusive flux. The scheme can keep local conservation of normal flux on the cell‐edge and can be used to deal with the case that the diffusive coefficients are discontinuous and anisotropic. In addition, no limiter is introduced. For the unsteady problem, the existence of a solution for the nonlinear discrete system is proved. Numerical results show that the new scheme has second order accuracy and can preserve the positivity. Abstract : A new positive finite volume scheme for the two‐dimensional convection‐diffusion equation on deformed meshes is proposed. The approximation of the convective flux is based on some available information of the diffusive flux. The scheme can keep local conservation of normal flux on the cell‐edge and can be used to deal with the case that the diffusive coefficients are discontinuous and anisotropic. In addition, no limiter is introduced. For the unsteady problem, the existence of a solution for the nonlinear discrete system is proved. Numerical results show that the new scheme has second order accuracy and can preserve the positivity.