A note on splitting errors for advection-reaction equations

A Note on Splitting Errors for Advection-Reaction Equations

In this note we consider proper ways to combine numerical schemes for advective transport and nonlinear chemistry. Obvious combinations are obtained with splitting in a so-called fractional step approach. We shall discuss for this approach correct implementations of source terms and innow boundary conditions. Further we consider the use of multistep methods with explicit treatment of the advect...

Maccormack's Method for Advection-reaction Equations

MacCormack's method is an explicit, second order nite diierence scheme that is widely used in the solution of hyperbolic problems. Here, we consider MacCormack's method applied to the linear advection equation with nonlinear source term. Various features of the method are analysed. First, we show that the conventional implementation is not stable for Courant numbers close to one unless a small ...

A Note on Viscous Splitting of Degenerate Convection-diffusion Equations

We establish L convergence of a viscous splitting method for nonlinear possibly strongly degenerate convection-di usion problems. Since we allow the equations to be strongly degenerate, solutions can be discontinuous and they are not, in general, uniquely determined by their data. We thus consider entropy weak solutions realized by the vanishing viscosity method. This notion is broad enough to ...

Numerical Solution of Advection-Diffusion-Reaction Equations

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...