Rajamäki, Markku; Saarinen, Mika Accurate one-dimensional computation of frontal phenomena by PLIM. (English) Zbl 0798.76068 J. Comput. Phys. 111, No. 1, 62-73 (1994). 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 Keywords:hyperbolic partial differential equations; piecewise linear interpolation method; strong convection problem; convection-diffusion problem; reaction-diffusion problem; approximate hyperbolic equations technique PDFBibTeX XMLCite \textit{M. Rajamäki} and \textit{M. Saarinen}, J. Comput. Phys. 111, No. 1, 62--73 (1994; Zbl 0798.76068) Full Text: DOI