A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

Abstract

We present a semi-Lagrangian method for integrating the three-dimensional incompressible Navier-Stokes equations. We develop stable schemes of second-order accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart.

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Document Details

Document Type
Technical Report
Publication Date
Nov 09, 2001
Accession Number
ADA460652

Entities

People

  • Dongbin Xiu
  • George Karniadakis
  • Jin Xu

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Applied Mathematics
  • Channel Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Diffusion
  • Equations
  • Errors
  • Flow
  • Navier Stokes Equations
  • Reynolds Number
  • Simulations
  • Three Dimensional
  • Turbulence
  • Turbulent Flow

Fields of Study

  • Physics

Readers

  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.

Technology Areas

  • Space