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March 29, 2017, 20:43 
Minmod Limiter

#1 
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I'm trying to implement a simple minmod limiter on my primitive variables.
It (seemingly) works perfectly when advecting a square pulse (u=p=const) but is worse than piecewise constant at Sod's problem (see pics). Here is how I'm calculating the edge states: Code:
leftDiff = rho[i1]  rho[i2]; rightDiff = rho[i]  rho[i1]; left.rho = rho[i1] + 0.5 * minmod(leftDiff, rightDiff); //... leftDiff = rho[i]  rho[i1]; rightDiff = rho[i+1]  rho[i]; right.rho = rho[i] + 0.5 * minmod(leftDiff, rightDiff); //... 

March 29, 2017, 22:07 

#2 
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Michael Prinkey
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I guess it depends on what you are doing in your "minmod" function. I am used to seeing fluxes interpolated based on:
phi_f = phi_0 + 0.5*psi(r)*(phi_0  phi_1) where r = (phi_1  phi_0)/(phi_0  phi_1) and for minmod, psi(r) = max(0,min(1,r)) (This all assumes evenly spaced grids. Also, I am used to using slope limiters on unstructured meshes, so my fluxlimiter Fu is a little rusty.) if your minmod performs those same calculations and returns a dimensional value for density, then it should be right. But r in the forms I am used to seeing is dimensionless, as is the return value of minmod(). So, I'd expect a trailing factor of units of density to make it physical in your right.rho and left.rho lines. 

March 30, 2017, 07:42 

#3  
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Quote:


April 2, 2017, 13:46 

#4 
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I think your problem does not come only from 2nd order reconstruction. Your 1st order solution does not look TVD to me, large oscillations near the shock do not occur when using shock capturing upwind fluxes. What spatial discretisation are you using ?


April 2, 2017, 14:12 

#5 
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Filippo Maria Denaro
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I agree, Godunov must give a monotonic solution


April 3, 2017, 09:04 

#6 
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I'm using finite volume. What kind of things can I do to find the problem?


April 3, 2017, 09:30 

#7 
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What Riemann solver are you using ? If it is the exact or Roe flux, maybe you should start with the simplest one: the Rusanov flux. As it seems that the raréfaction and contact are Well captured it may be à bug with the définition of left and right pressure as they are discontinuous across the shock


April 3, 2017, 12:04 

#8  
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April 3, 2017, 15:08 

#9 
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Hello,
I haven't looked much the code you are referring to. I can't recommend you taking pieces of code as a black box, the mistake could be in that code, the way you use it or both. It is worth taking time to learn how the exact solution is built (Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics is one of the references) and how approximate solvers have been derived. This way you will understand the code you mention and find what is wrong. Cheers, François 

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euler, limiter, minmod, plm, sod 
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