High Order Numerical Methods for Long Time Solutions with Discontinuities

Abstract

This project is about the design, analysis and application of high order accurate and nonlinearly stable finite difference (including finite volume) WENO schemes, finite element discontinuous Galerkin methods, and spectral algorithms for computing solutions of partial differential equations which are either discontinuous or with sharp gradients. Algorithm development, theoretical study about stability and convergence of the algorithms, investigation about efficient implementation including parallel implementations, and applications in compressible and incompressible gas dynamics and in semiconductor device simulations. are performed. The achievement strengthens our objective to obtain powerful and reliable high order numerical algorithms and use them to solve problems containing discontinuous solutions, especially those of Army interest.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2001
Accession Number
ADA395323

Entities

People

  • Chi Wang Shu

Organizations

  • Brown University

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Euler Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Galerkin Method
  • Gas Dynamics
  • Mathematics
  • Numerical Analysis
  • Physics
  • Semiconductor Devices
  • Semiconductors
  • Simulations
  • Two Dimensional

Readers

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

Technology Areas

  • Microelectronics