A Dynamically Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations - Validation and Model Problems

Abstract

We describe an algorithm for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid method based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. Using an approximation to the local truncation error to control the refinement, we use a form of domain decomposition to introduce patches of finer grid wherever they are needed to ensure an accurate solution. This refinement strategy is completely local: regions that satisfy our tolerance are unmodified, except when they must be refined to maintain reasonable mesh ratios. This locality has the important consequence that boundary layers and other regions of sharp transition do not steal mesh points from surrounding regions of smooth flow, in contrast to moving mesh strategies where such stealing is inevitable.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1991
Accession Number
ADA240141

Entities

People

  • C. P. Thompson
  • G. K. Leaf
  • J. Van Rosendale

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Differential Equations
  • Equations
  • Estimators
  • Flow
  • Flow Visualization
  • Fluid Dynamics
  • Geometry
  • Incompressible Flow
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Reynolds Number

Readers

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