Very Efficient High-order Hyperbolic Schemes for Time-dependent Advection Diffusion Problems: Third-, Fourth-, and Sixth-order

Abstract

In this paper, we construct very efficient high-order schemes for general time-dependent advection diffusion problems, based on the first-order hyperbolic system method. Extending the previous work on the second-order time-dependent hyperbolic advection diffusion scheme (Mazaheri and Nishikawa, NASA/TM-2014-218175, 2014), we construct third-, fourth-, and sixth-order accurate schemes by modifying the source term discretization. In this paper, two techniques for the source term discretization are proposed; (1) reformulation of the source terms with their divergence forms and (2) correction to the trapezoidal rule for the source term discretization. We construct spatially third- and fourth-order schemes from the former technique.

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Document Details

Document Type
Technical Report
Publication Date
Jul 07, 2014
Accession Number
ADA618447

Entities

People

  • Alireza Mazaheri
  • Hiroaki Nishikawa

Organizations

  • National Institute of Aerospace

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Boundaries
  • Boundary Layer
  • Coefficients
  • Computations
  • Computers
  • Convergence
  • Diffusion Coefficient
  • Eigenvalues
  • Equations
  • Error Analysis
  • Errors
  • Grids
  • Linear Systems
  • Reynolds Number
  • Steady State

Fields of Study

  • Mathematics

Readers

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