Numerical analysis of one dimensional motion of magma without mass forces

Abstract

In this paper, we present numerical treatment for a compaction-driven Darcian flow viscoelastic rock magma model. This problem is a strongly coupled system of one quasi-linear parabolic equation and one integro-differential equation for the density and the porosity of the flow. The numerical discretization uses cell-centered finite difference method, combined with semi-implicit and implicit time stepping. Implicit–explicit schemes, as well as implicit–explicit iterative algorithms have been developed to solve the corresponding discrete problems. Some properties (positivity, boundness, conservation) of the numerical solutions are investigated. Convergence study of the iteration processes is also presented. The efficiency and the accuracy of the proposed methods are illustrated numerically by test examples with near-real data.