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Lan, Bin; Sheng, Zhiqiang; Yuan, Guangwei

A new positive finite volume scheme for two-dimensional convection-diffusion equation. (English) Zbl 07805127

ZAMM, Z. Angew. Math. Mech. 99, No. 2, Article ID e201800067, 13 p. (2019).
Summary: 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.
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Cited in 6 Documents

MSC:

65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65-XX Numerical analysis
76Nxx Compressible fluids and gas dynamics

Keywords:

convection-diffusion equation; deformed meshes; nonlinear; positivity
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