Assessing the Quality of Curvilinear Coordinate Meshes by Decomposing the Jacobian Matrix,

Abstract

An algebraic decomposition of the Jacobian matrix relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. This decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. An full potential code TAIR is given in abbreviated form. The variables introduced here, and their derivatives are also natural Lagrange multipliers for adaptive mesh algorithms based on a variational principle. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1982
Accession Number
ADP001003

Entities

People

  • G. David Kerlick
  • Goetz H. Klopfer

Organizations

  • Nielsen Engineering & Research (United States)

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Aspect Ratio
  • Coordinate Systems
  • Decomposition
  • Demographic Cohorts
  • Differential Equations
  • Equations
  • Grids
  • Partial Differential Equations
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Ocean-Atmosphere Mesoscale Modeling, Data Assimilation, and Flux Boundary Layers