A High-Resolution Rotated Grid Method for Conservation Laws with Embedded Geometries (Preprint)

Abstract

We develop a second-order rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using a underlying Cartesian grid. Stability for time steps adequate for the regular part of the grid is obtained by increasing the domain of dependence of the numerical method near the embedded boundary by constructing h-boxes at grid cell interfaces. We describe a construction of h-boxes that not only guarantees stability but also leads to an accurate and conservative approximation of boundary cells that may be orders of magnitude smaller than regular grid cells. Of independent interest is the rotated difference scheme itself, on which the embedded boundary method is based.

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Document Details

Document Type
Technical Report
Publication Date
Mar 25, 2004
Accession Number
ADA640547

Entities

People

  • Christiane Helzel
  • Marsha J. Berger
  • Randall J. LeVeque

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Availability
  • Boundaries
  • Classification
  • Construction
  • Contracts
  • Geometry
  • Guarantees
  • High Resolution
  • Information Operations
  • Instructions
  • Monitoring
  • New York
  • Rotation
  • Security

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Distributed Systems and Data Platform Development
  • Geodesy