Numerical Theory and Implementation OpenFoam

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 October 24, 2021, 06:33 Numerical Theory and Implementation OpenFoam #1 Member   qutadah Join Date: Jun 2021 Location: Germany Posts: 92 Rep Power: 3 Hello, I have a question regarding how openfoam solves equations for simulation. If someone can guide me through my thought process and tell me if its right... Please point me out if I have mistakes in my understanding. 1- we have a computational mesh or domain which we know with its vertices or nodes. 2- Discretize the NS equations using the FVM approach and make a local equation for each cell in the mesh using one of the discretization methods for each term in the equation. All will be cell-centered based. 3- Interpolation methods is used for the diffusion term and only that term to find the face values because we need them in the equation. 4- we need to make a global matrix and solve it iteratively using one of the iterative solvers, where we under-relax specific terms if they increase instability in solving our matrix. Where does preconditioning come into all of this? *constructing a global matrix of 3 million cells in a steady state incompressible flow means we have 4 unknowns at each cell, which means 12 million unknowns in the equation? 5- We use one of the Algorithms to solve the pressure/velocity coupled momentum and continuity equations, and find the respective fields for each. 6- We solve using Initial and boundary conditions in our 0/ folder, however these values are also cell-centered. 7- nonorthogonal correctors are used to determine how many times the pressure equation is solved in a pressure/velocity coupling algorithm like the simple/piso. 8- we keep solving until we get a converged solution based on our residuals. Thanks!!

 Tags algorithm, numerical analysis, openfoam-6, theory