A Robust Solver for Incompressible Flow on Cartesian Grids with Colocated Variables

Abstract

We describe a second-order finite-volume formulation for solving incompressible flow problems on Cartesian grids using a colocated arrangement of variables. A projection method is used, in which a provisional cell-centered velocity is obtained by integrating the effects of advection and viscous forces over the numerical time step. Interface velocities are then interpolated from the provisional cell-centered velocities and corrected using the solution of a Poission equation for the pressure distribution. The cell-centered velocities are then interpolated from the corrected interface velocities. This pair of interpolation steps adds numerical diffusion that mimics a normal viscous stress, and the form of this damping term is similar to that which comes from stabilizing the Poisson equation for pressure by adding a term that is proportional to the fourth-derivative of pressure. The method requires no extra damping terms in order to maintain stability.

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Document Details

Document Type
Technical Report
Publication Date
Jul 13, 2005
Accession Number
ADA438536

Entities

People

  • Carolyn R. Kaplan
  • David R. Mott
  • Elaine Oran

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Advection
  • Computational Fluid Dynamics
  • Diffusion
  • Equations
  • Flow
  • Fluid Dynamics
  • Geometry
  • Incompressible Flow
  • Interpolation
  • Military Research
  • Physics
  • Poisson Equation
  • Pressure Distribution
  • Pressure Gradients
  • Simulations
  • Steady State
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Control Systems Engineering.