Mobile and immobile gaseous transport: Embedded analytical solutions to finite volume methods

Abstract

The motivation is driven by deposition processes based on chemical vapor problems. The underlying model problem is based on coupled transport–reaction equations with mobile and immobile areas. We deal with systems of ordinary and partial differential equations. Such equation systems are delicate to solve and we introduce a novel solver method, that takes into account ways to solve analytically parts of the transport and reaction equations. The main idea is to embed the analytical and semianalytical solutions, which can then be explicitly given to standard numerical schemes of higher order. The numerical scheme is based on flux‐based characteristic methods, which is a finite volume method. Such a method is an attractive alternative to the standard numerical schemes, which fully discretize the full equations. We instead reduce the computational time while embedding fast computable analytical parts. Here, we can accelerate the solver process, with a priori explicitly given solutions. We will focus on the derivation of the analytical solutions for general and special solutions of the characteristic methods that are embedded into a finite volume method. In the numerical examples, we illustrate the higher‐order method for different benchmark problems. Finally, the method is verified with realistic results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012