Test Problems

Workshop Discussion on Multiphysics Exemplars and Benchmarks

The document First Steps Toward a Multiphysics Exemplars and Benchmarks Suite is a modest start at a collection of multiphysics test problems.

Below are pointers provided by workshop participants to additional test problems that are relevant for multiphysics simulations.  

Fluid-structure interaction:  suggested by M. Mehl

http://www.featflow.de/en/benchmarks/cfdbenchmarking/fsi_benchmark.html

Comment: A variation of these problems has been done both in

Climate: suggested by K. Evans

paper that presents shallow water test cases:

http://www.sciencedirect.com/science/article/pii/S0021999105800166

3D test case: (hydrostatic- long time integration so appropriate for climate):

http://www.gfdl.noaa.gov/bibliography/related_files/ih9401.pdf

suite of test cases for 3D idealized atmosphere:

http://www-personal.umich.edu/~cjablono/dycore_test_suite.html

Aquaplanet test case is closest to actual atmospheric model run; has cloud physics but no land surface model:

Neale and Hoskins (2001). Atmos. Sci. Lett.. 1 doi:10.1006/asle.2000.0019

C. Jablonowski is an active developer of new test cases for the global atmospheric models:

http://www-personal.umich.edu/~cjablono/

High-order CFD workshop with test cases: suggested by E. Constantinescu

http://www.public.iastate.edu/~zjw/hiocfd.html

Short course by D. Estep

http://www.stat.colostate.edu/~estep/research/preprints/stabadjuncertain_2.pdf

Comment: Contains several examples, including the Brusselator problem, conjugate heat transfer, and others.

Nuclear waste disposal: suggested by B. Riviere

The COUPLEX Test Cases: Nuclear Waste Disposal Simulation, A. Bourgeat, M. Kern, S. Schumacher, J. Talandier, Computational Geosciences, volume 8, number 2, pages 83-98, 2004.

Problems for analysis:  suggested by B. Riviere

Relevant reference: Ern and Proft, International J. of Numer. Analysis and Modeling, 3, p.94-114, 2004, and references within.

Comment:  To be able to do a rigorous analysis, the multiphysics problems should be fairly simple.  I suggest looking at coupling hyperbolic with parabolic equations.  In some subdomains, a parabolic equation is solved, while in the other subdomains, an hyperbolic problem is solved. Along the convection direction, the exact solution is not continuous on some interfaces between the regions. 

Suggested by R. Pawlowski:  

The Brusselator problem is very rich and well documented.

A paper by Derby and Yeckel has a nice analytic 2D thermal problem: Journal of Computational Physics 228 (2009) 8566–8588

A Ropp and Shadid paper for a generic advection/diffusion/reaction: Journal of Computational Physics 228 (2009) 3508–3516

A simple FSI problem using a piston/spring system by Michler et al.: Computers & Fluids 33 (2004) 839–848

Test problems for LIME -- not yet released

Suggested by J. Brown:

http://59A2.org/na/KausMuehlhausMay-StabilizationGeodynamicFreeSurface-2010.pdf

Comment:  The paper below has two model setups. I suggest using the setup described in Figure 2 because it's simpler, but still exhibits the coupling challenges. Although the correction described in this paper is a significant improvement on the status quo, it still has a stability constraint that is less than the advective CFL.

Suggested by R. Maxwell:

paper:  M. Sulis, S. Meyerhoff, C. Paniconi, C., R. Maxwell, M. Putti and S. Kollet, A comparison of two physics-based numerical models for simulating surface water-groundwater interactions, Advances in Water Resources 

workshop: http://igwmc.mines.edu/workshop/intercomparison.html

Suggested by K. H. Lee:

Analytical solutions to advection and shock tube problem:  http://handle.dtic.mil/100.2/ADP010705

Experimental data to a pitching airfoil flutter case:  http://www.dtic.mil/dtic/tr/fulltext/u2/p010713.pdf