High-Order CESE Methods for Solving Hyperbolic PDEs (Preprint)

Abstract

In the present paper, we extend Chang's high-order method for system of linear and non-linear hyperbolic partial differential equations. A general formulation is presented for solving the coupled equations with arbitrarily high-order accuracy. To demonstrate the formulation, several linear and non-linear cases are reported. First, we solve a convection equation with source term and the linear acoustics equations. We then solve the Euler equations for acoustic waves, a blast wave, and Shu and Osher's test case for acoustic waves interacting with a shock. Numerical results show higher-order convergence by continuous mesh refinement. The new high-order CESE method shares many favorable attributes of the original second-order CESE method, including: (i) compact mesh stencil involving only the immediate mesh nodes surrounding the node where the solution is sought, (ii) the CFL stability constraint remains to be the same, i.e., < or = 1, as compared to the original second-order method, and (iii) shock capturing capability without using an approximate Riemann solver.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 03, 2011
Accession Number
ADA546869

Entities

People

  • David L. Bilyeu
  • Jean Luc Cambier
  • S. J. Yu
  • Yung-yu Chen

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Acoustic Waves
  • Air Force Research Laboratories
  • Blast
  • Blast Waves
  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Convergence
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Partial Differential Equations
  • Physics
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

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