ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 67, 1 (1998)
pp. 137-157

MAXIMUM PRINCIPLE AND LOCAL MASS BALANCE FOR NUMERICAL SOLUTIONS OF TRANSPORT EQUATION COUPLED WITH VARIABLE DENSITY FLOW
P. FROLKOVIC

Abstract. A parabolic convection-diffusion equation of the transport in porous media strongly coupled with a flow equation through a variable fluid density is studied from the point of view of the qualitative properties of numerical solution. A numerical discretization is based on ``node-centered'' finite volume methods with a clear form for a local mass balance property. Numerical solutions of the discrete conservation laws fulfill a discrete maximum (and minimum) principle. The presented results are an extension of ones in Ref. pat80, Ref. ike83 and Ref. ang95 for the case of transport equation coupled with variable density flow including the source/sink terms, inflow/outflow boundary conditions and anisotropic diffusion and for the case of upwind algorithms applied to a general class of finite volume meshes.

AMS subject classification. 65M60; Secondary 80A20
Keywords. Parabolic convection-diffusion equations, finite volume methods, upwind, artificial diffusion, discrete maximum principle, conservation laws

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Acta Mathematica Universitatis Comenianae
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Comenius University
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