Discuss the: -Motivation for introducing the upwind schemes of Godunov as a method of solution. -Requirements for different...

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Mechanical Engineering

Discuss the:
-Motivation for introducing the upwind schemes of Godunov as amethod of solution.
-Requirements for different pressure correction equations in aniterative solution process.
-Means for having velocity-to-pressure coupling, and thenpressure-to-density coupling.

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1 First order upwind schemeThis is the simplest numerical scheme It is the method that weused earlier in the discretization exampleWe assume that the valueof the face is the same as the cell centered value in the cellupstream of the face The main advantages are that it is easy toimplement and that it results in very stable calculations but italso very diffusive Gradients in the flow field tend to be smearedoutscheme summary2Requirements for different pressurecorrection equations in an iterative solution process3 PressureVelocity CouplingThe pressurebased solver allows you to solve your flow problemin either a segregated or coupled manner FLUENTprovides the option to choose among five pressurevelocity couplingalgorithms SIMPLE SIMPLEC PISO Coupled and for unsteady flowsusing the noniterative time advancement scheme NITA FractionalStep FSM All the aforementioned schemes except the coupledscheme are based on the predictorcorrector approachNote that SIMPLE SIMPLECPISO and Fractional Step use thepressurebased segregated algorithm while Coupleduses the pressurebased coupled solverSegregated AlgorithmsSIMPLEThe SIMPLE algorithm uses a relationship between velocity andpressure corrections to enforce mass conservation and to obtain thepressure fieldIf the momentum equation is solved with a guessed pressure field the resulting face flux then1does not satisfy the continuity equation See Answer

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