Incompressible Spectral-Element Method-Derivation of Equations
Abstract
A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (non- linear, pressure, viscous) schemes. The non-linear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the non-linear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient, By combining this predicted pressure gradient with the non-linear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity. Numerical, Spectral-element method, Computational fluid dynamics
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1993
- Accession Number
- ADA266374
Entities
People
- Russell G. Deanna
Organizations
- National Aeronautics and Space Administration