WENO accuracy study, a 2D test case?
Hi,
Is there a standard 2D test case to perform accuracy study of WENO without using periodic boundary conditions? I know that people do tests with periodic BC, but I would like to understand if the boundary effects could decrease convergence rate significantly. Say, for example in a scalar convection case? Is there a paper or a reference to check with that? Thanks 
Try with 2D Reimann problems.
A large list can be found in the paper "Solution of 2d Reimann problems for Gas Dynamics without Reimann Problem Solvers" A. Kurganov, E. Tadmor 
Hello,
The advantage of periodic bc is that you can simulate a long time/distance advection case and then more easily show the less diffusive properties of high order schemes. Without periodic bc, you would need a much wider grid and computational time would be much higher. If you do not want to work with such a bc, you can still perform accuracy test with advection equation to check the formal order of accuracy of your scheme. But you have to be very careful on the treatment of the limit as indeed it will spoil the observed order of accuracy for finer grids. What I am used to do is to prescribe the exact Riemann state (from the exact solution) at the face gauss nodes and let the Riemann solver do the job. François 
More test cases for viscous flows
Hi,
I have a 2d WENO code for compressible viscous flows and looking for test cases to run it on. I tried running on the lid driven cavity problem but couldnt get it to converge. Can you suggest some other test cases which are simple to set up like the Reimann problems but for viscous flows? 
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Start first with a classical test on the Euler equations, you can also have a look to the book of LeVeque. 
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I have ran tests with inviscid flow on 2d reimann problems and have got acceptable results. I just wanted to check my results after adding the viscous terms, thereby making it a full Navier Stokes solution. So yes, i need some simple test cases for the NS equations. 0012 is a widely used test case which i dont want to attempt as it would take a lot of time to just set up the grid and transformations. I will have a look at the book you mentioned but please do tell me if you know of any easy test cases for NS solver. Thanks. 
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That strongly depends if you are interested in testing the capability of your code in solving flows with relevant compressibility effects or not. If your code can solve low Mach flows, you can use standard testcases for incompressible flows (Taylor solution, backward facing step flow, etc). 
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Also, I am using rho_inf*u_inf^2 to non dimensionalise the pressure, so Mach number doesnt explicitly show up in the equations I am solving. Would that cause any problems or should I go for the conventional 1/(gamma*M_inf^2) which is typically followed in highspeed flow literature? My final aim is to study shock wave boundary layer interactions so I would be running the final code at high Mach numbers. 
Mach number appears intrinsically as a response between the density and pressure variation. For a low Mach number flow, some codes use preconditioning techniques. But I see some codes working without that.
Try first a steady laminar flow in a channel, for example as described here http://acoustics.ae.illinois.edu/pdf...lele1992.pdf 
try also searching here https://www.cfdonline.com/Wiki/Vali...2D_test_cases

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How good would be a Taylor Green Vortex (2d) as a test case? With periodic boundary conditions i am getting a drift of the vortex and it doesnt match at all with the theoretical (exponential decay) solution. So i am confused as some test case (2d Reimann inviscid gives good results while others (Taylor vortex) isnt even near to what i expect. 
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Weno
I don't mean to be off topic, but when using WENO for incompressible NS. If I want to discretize the nonlinear advection term, do I need to use a hyperbolic scheme on top of WENO or can I just perform WENO on the nonlinear terms? In compressible cases you see Local Lax Friedrichs + WENO (for example.)

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