Nonlinear Multigrid for the Euler Equations: The One-Dimensional Scalar Case,

Abstract

A recent multigrid method for computing steady inviscid compressible flow is analyzed for the one-dimensional scalar case. The discretization in space by means of upwind differencing has first- or second-order accuracy. Three types of relaxation schemes that use only local information are examined. A numerical experiment with a smooth steady solution shows good agreement with the estimated damping rates. A discontinuous solution displays slower convergence. This is mainly caused by the singularity at the shock. The singularity can be removed by the additional constraint of local conservation, which is achieved through a special kind of local relaxation, using information about conservation from coarser grids. The sonic point causes some slow-down as well, but this can be neglected in practical applications. It turns out that a first-order-accurate solution can be obtained by 1 F-cycle per grid, whereas second-order accuracy requires about 4.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 09, 1986
Accession Number
ADA173369

Entities

People

  • William A. Mulder

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Cell Size
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Programs
  • Difference Equations
  • Differential Equations
  • Equations
  • Euler Equations
  • Flow
  • Fluid Dynamics
  • Gas Dynamics
  • Growth Factors
  • Physical Properties
  • Steady State
  • Two Dimensional

Fields of Study

  • Physics

Readers

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

Technology Areas

  • Space