On the marching solution of elliptic equations in viscous fluid mechanics
Abstract
Marching solutions for the Poisson equation and for a set of linearized parabolized Navier-Stokes equations are considered. Enhancement of stability by high order derivatives is investigated, in order to find their influence on the accuracy and the extent of the region of integration. The results indicate that the addition of a mixed fourth order derivative damps instabilities and allows longer integration distance but may reduce the accuracy. Higher order mixed derivatives are more effective. Richardson extrapolation can be used to improve the accuracy of the stabilized solutions.
- Publication:
-
Numerical Methods in Laminar and Turbulent Flow
- Pub Date:
- 1981
- Bibcode:
- 1981nmlt.proc....3I
- Keywords:
-
- Computational Fluid Dynamics;
- Elliptic Differential Equations;
- Navier-Stokes Equation;
- Spatial Marching;
- Viscous Flow;
- Euler-Lagrange Equation;
- Finite Difference Theory;
- Fluid Pressure;
- Numerical Stability;
- Parabolic Differential Equations;
- Poisson Equation;
- Small Perturbation Flow;
- Fluid Mechanics and Heat Transfer