Semi-implicit methods based on inflow implicit and outflow explicit time discretization of advection

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Peter Frolkovič

Abstract

We introduce several numerical methods for the solution of advection equation using semi-implicit time discretization in which the inflow fluxes are discretized implicitly and the outflow fluxes explicitly. We derive the so called $\kappa$-scheme and show it is $2^{nd}$  order accurate and uncon\-ditionally stable in 1D and 2D case for tensor grids with a special choice of $\kappa$ giving $3^{rd}$ order accurate scheme for constant speed in 1D. Moreover, we present a $2^{nd}$ order accurate and unconditionally stable Corner Transport scheme in 2D case for tensor grids that is $3^{rd}$ order accurate for constant velocity. We discuss several improved properties of  these schemes when compared to analogous fully explicit and fully implicit schemes.

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FROLKOVIČ, Peter. Semi-implicit methods based on inflow implicit and outflow explicit time discretization of advection. Proceedings of the Conference Algoritmy, [S.l.], p. 165-174, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/405>. Date accessed: 22 sep. 2017.
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