High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains

Abstract

The overarching goal of this research was to construct stable, robust and efficient high order accurate computational methods for long time integration of nonlinear partial differential equations. High order accuracy methods (Spectral, Finite Difference and Finite Elements) for the numerical simulations of flows with discontinuities, in complex geometries were developed. In particular applications in supersonic combustion were emphasized. Specific research subjects included: Robust high order compact difference schemes, ENO and WENO schemes, discontinuous Galerkin methods, the resolution of the Gibbs phenomenon, parallel computing and high order accurate boundary conditions. In order to overcome the difficulties stemming from complicated geometries, we have developed multidomain techniques as well as spectral methods on arbitrary grids. Several multidimensional codes for supersonic reactive flows had been constructed as well as a library of spectral codes (Pseudopack).

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Document Details

Document Type
Technical Report
Publication Date
Nov 30, 1998
Accession Number
ADA380856

Entities

People

  • Chi‐Wang Shu
  • David Gottlieb
  • J. Hesthaven
  • P. F. Fischer
  • W. S. Don

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Convection
  • Differential Equations
  • Equations
  • Galerkin Method
  • Geometry
  • Navier Stokes Equations
  • Partial Differential Equations
  • Simulations
  • Supersonic Combustion
  • Three Dimensional
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Hypersonics