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The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. p*, u*, v* are guessed Pressure, X-direction velocity and Y-direction velocity respectively, p', u', v' are the correction terms respectively and p, u, v are the correct fields respectively; Φ is the property for which we are solving and d terms are involved with the under relaxation factor.
SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems. [1]
It is an extension of the SIMPLE algorithm used in computational fluid dynamics to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the Navier-Stokes equations developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.
The stability of the selected discretisation is generally established numerically rather than analytically as with simple linear problems. Special care must also be taken to ensure that the discretisation handles discontinuous solutions gracefully. The Euler equations and Navier–Stokes equations both admit shocks and contact surfaces.
The idea of pressure-correction also exists in the case of variable density and high Mach numbers, although in this case there is a real physical meaning behind the coupling of dynamic pressure and velocity as arising from the continuity equation
Any existing fluid solver can be coupled to a solver for the fiber equations to solve the Immersed Boundary equations. Variants of this basic approach have been applied to simulate a wide variety of mechanical systems involving elastic structures which interact with fluid flows.
COMSOL Multiphysics is a finite element analyzer, solver, and simulation software package for various physics and engineering applications, especially coupled phenomena and multiphysics. The software facilitates conventional physics-based user interfaces and coupled systems of partial differential equations .
In the MP-PIC method, the fluid motion is coupled with the particle motion through , the rate of momentum exchange per volume between the fluid and particle phases. The fluid phase equations are solved using a finite volume approach.