Entropy Schemes for One-Dimensional Convection-Diffusion Equations
Keyword(s):
In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy.
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