hi

i need to understand what parabolic, elliptic and hyperbolic equations exactly mean? and what are their implications in CFD. Thnx in advance

Arnie

Hi Arnie,

It depends on the application and problem you take into onsideration for solving which inturn dependent upon the boundary conditions used.

Moreover the implementation of these equations are used in mesh generation also.

Karthik

A hyperbolic equation is a pde whose characteristics are all real and distinct. An example of which is the wave equation.

An elliptic equation is one with no real characteristics such as Laplaces equation.

A parabolic equation is one with only one real characteristic such as the heat equation.

For more details you should look at an introductory book on pdes. Basically the type of the pde determines what the correct initial/boundary conditions should be applied and hence determines the type of numerical method to be used.

For CFD observe that the inviscid (unsteady) Euler equations are hyperbolic, the unsteady Navier-Stokes equations are parabolic and the steady state Navier-Stokes equations are elliptic. The steady state Euler equations are either elliptic or hyperbolic depending upon whether the flow is subsonic or supersonic respectively.

Thanks Karthik n Tom, I wud look further in A PDE book. Arnie