Low Machnumber Problem
Hello,
I'm working on the modellisation of lowmach flows of perfect gas, and I'm facing on an airfoil Naca0012 a surprising result. My CFD Code is a compressible one and the mesh is unstructured (the finitevolume timeintegration can be explicit or implicit) The publications predict that in lowmach flow (Mach from 0.1 to 0.00001) the pressure scale is proportional to Ma. As a consequence the numerical dissipation (Roe's method) has to be preconditioned (Elie Turkel) in order to obtain a scale proportional to Ma*Ma. But my results with a classic Roe's method, without any preconditioning, are giving a pressure scale proportional to Ma*Ma !! That means my compressible Code is able to deal with incompressible flows of compressible fluids without any preconditioning. That's the contrary of the works of Viozat! And I don't understand why my computation is so accurate. Besides my results without preconditioning are the same that those of Viozat (with preconditioning). Finally I have observe completly different results with the HLL method. Has someone an idea of what can explain such a good behaviour of my Roe's method ? (I don't think it's a computational error since the results are coherents.) 
Re: Low Machnumber Problem
What? That is unbelivable!!
I have been working on the CFD code development with the preconditioning method employing Roe FDS and AUSM class. In my cases, if I don't use preconditioning, simulation results are not acceptable at low Mach flow regime, below Ma < 0.1. If your result is true, many unresolved problems related to preconditioning method, such as numerical instability at the stagnation point, will be resolved. 
Re: Low Machnumber Problem
Try Wiess and Smith preconditioner, we have used for very low mach numbers, worked very well, only problem is at very high speed flow above mach 23. If I am correct the paper is in 1995 AIAA Journal for explicit method and 1997 for implicit method. or get hand of Fluent theory manual. you can get online by some google search.

Re: Low Machnumber Problem
That's very interesting. (I wouldn't rule out a freak mistake in the code, which might give you some unintended preconditioning, but that seems very unlikely).
Do you see any convergence problems at M<0.01 ? How well does your code predict the flow in the compressible case? How does the convergence for high Mach number compare to convergence at low M? Which integration method are you using? Are you using local time steps (which basically is a very simple form of preconditioning)? 
Re: Low Machnumber Problem
I haven't seen any convergence problem at Mach numbers down to 10^6. My code exploits weiss&smith preconditioner and roundoff error control proposed by choi&merkle.

Re: Low Machnumber Problem
That's cool. You should read the original post, though. This guy is claiming to have no problems without(!) any preconditioning.

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