High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

Abstract

The gas dynamics equations, coupled with a static gravitational field, admit the hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term. Many astrophysical problems involve the hydrodynamical evolution in a gravitational field, therefore it is essential to correctly capture the effect of gravitational force in the simulations. Improper treatment of the gravitational force can lead to a solution which either oscillates around the equilibrium, or deviates from the equilibrium after a long time run. In this paper we design high order well-balanced finite difference WENO schemes to this system, which can preserve the hydrostatic balance state exactly and at the same time can maintain genuine high order accuracy. Numerical tests are performed to verify high order accuracy, well-balanced property, and good resolution for smooth and discontinuous solutions.

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Document Details

Document Type
Technical Report
Publication Date
Nov 12, 2011
Accession Number
ADA557672

Entities

People

  • Chi-Wang Shu
  • Yulong Xing

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Computations
  • Dynamics
  • Equations
  • Equations Of State
  • Euler Equations
  • Fluids
  • Gas Dynamics
  • Gravitational Fields
  • Mathematics
  • Numerical Analysis
  • Pressure Distribution
  • Shallow Water
  • Simulations
  • Steady State
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics

Technology Areas

  • Space
  • Space - Orbital Debris