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Accurate one-dimensional computation of frontal phenomena by PLIM. (English) Zbl 0798.76068

Summary: We introduce a new method for solving systems of one-dimensional hyperbolic partial differential equations and present the first applications of this method. The piecewise linear interpolation method PLIM is shown to have the capability to preserve the shape of a propagating distribution and great applicability. Various difficult flow problems, such as the strong convection problem, the convection-diffusion problem, and the reaction-diffusion problem, have been solved. In addition, the approximate hyperbolic equations technique to handle the diffusion terms is introduced.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R50 Diffusion
76R99 Diffusion and convection
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