Residual Scale Dependence and PDE Filters

Abstract

When the filter operation acting upon nonlinear partial differential equations (PDE) is examined by way of a PDE filter on a domain involving space/time and an additional dimension associated with a space scale parameter. Under this approach it is possible to obtain an estimate for the error associated with the equations satisfied by the filtered solutions of the microscopic scale PDE given any approximation of the residuals. This provides a condition of consistency. The PDE filter approach suggests approximations for the residuals that are independent of empirical or arbitrary, parameters. Here the main points two previous articles are presented with some additional issues addressed. An attempt is made to remain within a setting of general nonlinear PDE systems. The filtered equations of reactive turbulent flows are presented as an example.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2001
Accession Number
ADP013639

Entities

People

  • G. Pantelis

Organizations

  • University of Sydney

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Chemical Kinetics
  • Coordinate Systems
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of Motion
  • Filters
  • Flow
  • Flow Fields
  • Mechatronic Engineering
  • Models
  • Partial Differential Equations
  • Payload
  • Residuals
  • Technical Information Centers

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.

Technology Areas

  • Space