Adaptive Numerical-Dissipation/Filter Controls for High Order Numerical Methods

Abstract

Proper control of the numerical-dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical-dissipation/filter are not only physical problem dependent: but also vary from one flow region to another. An approach for the automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical-dissipation/filter for non-dissipative high order schemes is proposed. These scheme-independent sensors are capable of distinguishing shocks/shears, turbulent fluctuations and spurious high frequency oscillations. In addition, these sensors are readily available as an improvement over existing grid adaptation indicators. The same shock/shear detector that is designed to switch on the shock/shear numerical dissipation can be used to switch off the entropy splitting form of the inviscid flux derivative in the vicinity the discontinuous regions to further improve nonlinear stability and minimize the use of numerical dissipation. The rest of the sensors in conjunction with the local flow speed and Reynolds number can also be used to adaptively determine the appropriate entropy splitting parameter for each flow type/region. The goal of this paper is to further improve nonlinear stability, accuracy and efficiency of long-time numerical integration of complex shock/turbulence/acoustics interactions and numerical combustion. The minimization of employing very fine grids to overcome the production of spurious numerical solution and/or instability due to under-resolved grids is also sought.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2001
Accession Number
ADP013654

Entities

People

  • B. Sjoegreen
  • H. C. Yee

Organizations

  • National Aeronautics and Space Administration

Tags

Communities of Interest

  • Energy and Power Technologies
  • Sensors

DTIC Thesaurus Topics

  • Boundary Layer
  • Compressible Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Convection
  • Detectors
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Navier Stokes Equations
  • Numerical Analysis
  • Numerical Integration
  • Reynolds Number

Fields of Study

  • Physics

Readers

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