Parallel Multi-Scale Algorithms and Applications to Turbulence

Abstract

This report describes development of a new hierarchical spectral basis appropriate for hp-finite element formulations on unstructured grids consisting of triangular and tetrahedral subdomains. The new multi-resolution basis has the following properties: (1) Jacobi polynomials of mixed weights, (2) Semi-orthogonality, leading to great sparsity, (3) Hierarchical structure, (4) Generalized tensor products, (5) Mixed order expansions, which provides great flexibility in adaptive discretizations, and 6) Gauss-Jacobi quadratures that minimize errors in complicated geometries. The accuracy of this method has been tested in two and three dimensions. Importantly, numerical results verified that the new hierarchical basis exhibits convergence even for highly distorted meshes.

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Document Details

Document Type
Technical Report
Publication Date
Oct 09, 1997
Accession Number
ADA334848

Entities

People

  • George Karniadakis

Organizations

  • Brown University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Fluid Mechanics
  • Geometry
  • Mathematics
  • Mechanical Properties
  • Mechanics
  • Navier Stokes Equations
  • Polynomials
  • Turbulence
  • Two Dimensional

Readers

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