Department of Aerospace Engineering

CFD Center Seminar Series: Ganesh Rajagopalan, Professor of Aerospace Engineering, ISU; "Development of an Explicit Algorithm for Pressure Based Schemes"

 

This seminar will be held at 4:10 PM in Room 1235 Howe Hall

"Development of an Explicit Algorithm for Pressure Based Schemes"

The SIMPLE family of algorithms have popularized the pressure based schemes for incompressible flows. The effect of pressure on velocity is of primary importance in incompressible flows. However, pressure appears only as a source term in the momentum equations. The continuity equation implicitly dictates the pressure field and yet pressure is not a variable of the mass conservation equation. This predicament and its remedy well known by the name pressure velocity coupling is resolved in SIMPLE and its variants (SIMPLER, SIMPLEC) by obtaining an approximate pressure correction field, which is used iteratively to correct the velocity field and/or the pressure field seeking an overall satisfaction of the conservation equations. The approximate nature of the pressure correction equation is often attributed to convergence issues.

The new algorithm presented here is based on the fact that, if the pressure field is known the momentum equations can be solved, iteratively or otherwise, to obtain the velocity field correctly. An exact equation for the pressure field is obtained by manipulating the discretized mass and momentum equations. Once the pressure field is known the velocity is updated explicitly using the four stage Runge-Kutta algorithm without the need for iterating the momentum equations. As a test bed for the explicit algorithm, three different cases have been analysed: a polar driven cavity, a backward facing step, and a circular plate at 90 degrees incidence.

The Runge-Kutta algorithm converges well for all the cases presented.

 

 

 

 

 

 

 

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