Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions

Abstract

We have investigated high order finite difference weighted essentially non-oscillatory (WENO) schemes, finite volume WENO schemes and discontinuous Galerkin finite element methods, for solving partial differential equations with discontinuous or rapidly changing solutions. Algorithm development, analysis, implementation and applications have been carried out. Research has been performed in all areas listed in the original proposal, and progress and results consistent with the original objectives have been obtained. There are 53 refereed journal publications (42 appeared, 11 accepted and to appear) resulting from this project. These achievements have strengthened our objective to obtain powerful and reliable high order numerical algorithms and use them to solve convection dominated problems, especially those of army interest.

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Document Details

Document Type
Technical Report
Publication Date
Dec 06, 2007
Accession Number
ADA482375

Entities

People

  • Chi-Wang Shu

Organizations

  • Brown University

Tags

Communities of Interest

  • Advanced Electronics
  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Galerkin Method
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Semiconductor Devices
  • Shallow Water
  • Shock Waves
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Technical Research and Report Writing.