10-06-2017, 10:56 PM
Please provide the SIMPLE algorithm matlab code
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simple algorithm cfd matlab
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Please provide the SIMPLE algorithm matlab code
12-06-2017, 10:07 AM
In Computational Fluid Dynamics (CFD), the SIMPLE algorithm is a numerical procedure widely used to solve the Navier-Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for equations related to pressure.
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 widely used by many researchers to solve different types of fluid flow and heat transfer problems.
Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail. A modified variant is the SIMPLER algorithm (SIMPLE Revised), which was introduced by Patankar in 1979.
Algorithm
The algorithm is iterative. The basic steps for updating the solution are as follows:
1. Set the boundary conditions.
2. Calculate the velocity and pressure gradients.
3. Solve the discrete moment equation to calculate the intermediate velocity field.
4. Calculate uncorrected mass flows on faces.
5. Solve the pressure correction equation to produce pressure correction cell values.
6. Update the pressure field: ![[Image: bed1f59faf6e0eb8017ceb942d4c218931947515]](https://wikimedia.org/api/rest_v1/media/math/render/svg/bed1f59faf6e0eb8017ceb942d4c218931947515)
where urf is the sub-relaxation factor for the pressure.
where urf is the sub-relaxation factor for the pressure.7. Update the pressure limit corrections. ![[Image: 9f9ee1c96778e2d63114e625bb7746de47abc965]](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f9ee1c96778e2d63114e625bb7746de47abc965)
8. Correct the mass flows of face: ![[Image: 6e0ac5448409a36197edaa00d91e2b76139e7882]](https://wikimedia.org/api/rest_v1/media/math/render/svg/6e0ac5448409a36197edaa00d91e2b76139e7882)
9. Correct cell rates : ![[Image: 8cb61bd8e73fed2b0c44f3ee756bb069f9db0a1d]](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cb61bd8e73fed2b0c44f3ee756bb069f9db0a1d)
; Where ![[Image: ebe9c383e678dea1fa791c6e23a44ba7d32e34ac]](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe9c383e678dea1fa791c6e23a44ba7d32e34ac)
is the gradient of pressure corrections, ![[Image: 2cecb75e7e967b20bc919e317048c43805ab548c]](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cecb75e7e967b20bc919e317048c43805ab548c)
is the vector of central coefficients for the discretised linear system that represents the velocity equation and Vol is the cellular volume.
; Where is the gradient of pressure corrections, is the vector of central coefficients for the discretised linear system that represents the velocity equation and Vol is the cellular volume.10. Density of update due to changes in pressure.
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