An Augmented Approach for Stokes Equations With Discontinuous Viscosity and Singular Forces

Abstract

For Stokes equations with discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, the pressure is known to be discontinuous and the velocity is known to be non-smooth. It has been shown that these discontinuities are coupled together which makes it di cult to obtain accurate numerical solutions. In this paper, a second order accurate numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The Generalized Miminal Residual (GMRES) iterative method is used to solve the Schur complement system for the augmented variables which are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that fast Poisson solvers can be used in each iteration. Numeri- cal examples against exact solutions show that the new method has average second order accuracy in the infinity norm, and the number of GMRES iterations is independent of mesh sizes. An example of a moving interface problem is also presented.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2004
Accession Number
ADA446726

Entities

People

  • Kuzufumi Ito
  • Ming-chih Lai
  • Zhilin Li

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Computations
  • Coordinate Systems
  • Delta Functions
  • Differential Equations
  • Electronic Mail
  • Equations
  • Linear Regression Analysis
  • Mathematics
  • Navier Stokes Equations
  • North Carolina
  • Partial Differential Equations
  • Poisson Equation
  • Regression Analysis
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)