Implicit Solutions of the Unsteady Navier-Stokes Equation for Laminar Flow Through an Orifice,

Abstract

The Navier-Stokes and the continuity equations are rearranged into a vorticity transport equation and a definition of vorticity equation. One thus obtains two elliptical partial differential equations in the two variables of vorticity and stream function. Implicit finite difference forms of the equations are developed which are fourth-order accurate in space and second-order accurate in time. Grid networks were imposed on the flow field. Initial conditions were designated to be either (1) no flow in the case of the first time step or (2) the results from the previous time step. Solutions were obtained from one time step to the next by iterating the vorticity transport and definition of vorticity equations together with the appropriate boundary conditions.

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1974
Accession Number
ADA002454

Entities

People

  • David W. Coder

Tags

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Differential Equations
  • Equations
  • Flow
  • Flow Fields
  • Laminar Flow
  • Navier Stokes Equations
  • Partial Differential Equations
  • Transport Ships

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster