A numerical algorithm for simulation of two-component flows in the Earth's mantle
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.86001
author: Z. A. Liapidevskaya
author: V. E. Petrenko
publication date: 2001-12-13T00:00:00Z
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 86-08
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65N06
zbMATH DE Number: 1682240
zbMATH Keywords: geodynamics
zbMATH Keywords: slow convective flow
zbMATH Keywords: two-components flow
zbMATH Keywords: numerical simulation
MaRDI profile type: Publication
title: A numerical algorithm for simulation of two-component flows in the Earth's mantle
published in: Bulletin of the Novosibirsk Computing Center. Series: Mathematical Modeling in Geophysics
review text: In the framework of the model of a two-component isothermal viscous fluid, the authors study numerically slow convective flows in the Earth's mantle with characteristic scale \(1\) cm/year. Attention is focused on the construction of a numerical algorithm for solving the system of equations of the motion of a two-component high viscous fluid written in terms of stream function and vortex variables. A particular attention is paid to describing the difference method for solving a boundary value problem for the system obtained. The difference approximation for the Poisson equation is reduced to solving a system of linear algebraic equations with block three-diagonal matrix of coefficients. To solve the system, the authors apply the direct method based on using orthogonal reflection transformations. To construct the difference scheme for the equation of mass transport for the concentration of a mixture, the authors use the Gauss-Ostrogradskij theorem. The sequence of numerical representations of the resultant finite-difference problem is exposed as an algorithm. The rest of the article is devoted to numerical experiments.
reviewed by: Vladimir N. Grebenev
description: scientific article; zbMATH DE number 1682240