Preprint 2005-036

Explicit Solutions of a Convection-Reaction Equation and Defects of Difference Schemes

Youngsoo Ha and Yong-Jung Kim

Abstract: We introduce two kinds of explicit solutions to the convection-reaction equation,

ut+(|u|q/q)x=u,     u,x∈R, t∈R+, q>1,
and employ them to test properties of various computational schemes. From this test we observe that computed solutions using Lax-Friedrichs, MacCormack and Lax-Wendroff schemes break down in a finite time. On the other hand some other schemes including WENO, NT and Godunov show more stable behavior and the tests provide their detailed behaviors. It is discussed that if a numerical scheme is applied to this problem together with the splitting method, certain defects of the scheme can be magnified exponentially and observed easily. Sometimes such a behavior destroys the numerical solution completely and hence one need to pay extra caution to deal with reaction dominant systems.

Available as PDF (504 Kbytes).
Youngsoo Ha, <>
Yong-Jung Kim, <>
Publishing information:
submitted to J. Comput. Phys.
Submitted by:
<> September 23 2005.

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