Fvm: Fill & Download for Free

Firstly, come out of the myth that ‘CFD is based on FVM’.For your information, FVM is practised by most of the engineers/scientists in industry and academia for CFD. But, CFD is solely not based on FVM.In CFD, different discretization methods are used:Finite Difference(FD)Finite Volume(FV)Finite Element(FE)Spectral MethodsBoundary Element Method(BEM)Particle methods etcIn Aerospace domain for compressible flows, Finite Difference methods are preferred to Finite Volume methods, because compressible flow calculations, shock capturing etc require higher order numerical methods and taking FVM beyond 2nd order is highly difficult. Whereas, FDM can reach up to 5th and 7th order accuracy.In Mechanical & Chemical engineering fields, many problems involve incompressible flows. As mass conservation is inherent in FVM, it is preferred over other methods. For incompressible flows FVM is accurate over other methods, while it also depends on the class of problems.Finite Element methods were first originally made for structural analysis, but still can be applied for fluid flows and heat transfer applications with good accuracy.FDM, FVM, FEM are known as ‘Big 3’ because they are widely used. But, that’s not all of it.Other methods like Boundary element, spectral, particle methods are also used in the scientific community for specific class of complex problems where the ‘big 3’ are not sufficient to get desired results.Boundary element methods are used in Acoustics, Fluid Dynamics etc. Example: Studies on liquid sloshing.Spectral methods are generally preferred for non-linear problems in 3D complex geometries which uses Fast Fourier transforms to speed up the calculations where it plays computationally cheaper than FVM.There are also other method to calculate fluid flows such as Lattice Boltzmann Method(LBM), Immersed Boundary Method(IBM) for Fluid-Structure interaction; Vortex & Particle based methods, Smoothed Particle Hydrodynamics(SPH) etc.

Easy steps :JD Anderson & Gilbert Strang - Start Reading in Parallel for a period of 6 months each. (Solve derivations by hand couple of times)Move over to Hoffman and Chiang (2 to 3 months )to understand FDM and FVM intro and Start basic programming with FORTRAN and C++Move over to NPTEL courses from IIT Madras , Versteeg & Malalasekera for FVM incompressible and Learn SIMPLE scheme. (Find codes for SIMPLE online, there are many fortran and C++ codes for free) (2 months)Start reading E.D. Toro for FVM Compressible and Unstructured Grids. (Gilbert Strang will seem so helpful now…) (3 months)Try to make grids from ICEM tutorials. Rely on Youtube channels heavily and also CFD Onilne. Just clear yourself up for Y+ estimates.Pick up ansys and start with classic problems of - Channel Flow, Fully developed Poiseille Flow, Lid driven cavity flow, Forward facing step, backward facing step and general cavity flow. Study these test cases by downloading free research papers and CFD online and see how you can setup your cases in Ansys and get similar resutls with using similar standard ICs and BCs.Find some compresible codes using TVD WENO and MUSCL schemes and try applying different slope limiters in the code for FVM. (1 month)Write you own WENO code for a channel flow test case and Sod’s Shock tube test case. (2 months)This will lead you to Finite Element and unstructured Grids…. and you can come back for me to share more with you.

All the three are numerical methods for solving differential equations and divides the domain into sub domains like nodes, control volumes or sub domains.FDM determines the property at a single point/node. This method is the oldest of the three but now it has become obsolete.FVM determines the property over a control volume and assumes that it is concentrated in its geometric centre.FEM determines the property of an element. An element can consists of 2 or more than 2 nodes.FEM is used in the case of solids while FVM is used for fluids in research.FEM is not used for fluids because one of the meshing quality parameters of FEM called aspect ratio to be not less than 5:1. But, a fluid deforms more making the aspect ratio less than 5:1 in most of the cases. Hence, FEM is generally not used in case of fluids.