Benchmark+Anelastic+Sph.

=Benchmark for Anelastic Spherical Shell Dynamo Codes=

During the KITP program we hope to perform a benchmark for spherical anelastic spherical shell codes.

The idea is to bring together groups working on these issues to compare

(i) Numerical Techniques (ii) Different methods of solving the equations (iii) Establish a benchmark problem - simple, but which tests all the linear and non-linear terms for future codes to be compared with.

This Wiki page can be used as a repository for ideas, results etc, etc, even after the end of the KITP program

As a first step, those interested in participating in such a benchmarking scheme should sign below here.

Piotr Boroński Krzysztof Mizerski Gary Glatzmaier Chris Jones Benjamin Brown Allan Sacha Brun Steve Tobias Weijia Kuang Emmanuel Dormy Kirill Kuzanyan Jon Rotvig Mark Miesch

Piotr Boroński
 * (Leeds code)**

The first anelastic version of the "Leeds code" didn't have a magnetic field. This code was applied to number of HD configurations and hopefully Chris Jones will have some suggestions as for the sensitive configurations for the benchmark.

The anelastic MHD version of the code was completed only very recently and very few cases were studied so far. A presentation of the equations used in the present version of the anelastic "Leeds code" is accessible [|here]. So far we reproduced the Boussinesq benchmark configurations form the //Christensen et al.// (2001) paper and used one of these benchmark configurations as an initial state and then followed it increasing gradually the density contrast ratio to some a quite moderate values (approx. 3 - 5).

Suggestions/preferences for the benchmark (I would opt for equations/boundary conditions as simple as possible):
 * 1) constant turbulent viscosity and magnetic diffusivity coefficients
 * 2) entropy formulation
 * 3) no "nabla T" term - only "T nabla S"
 * 4) boundary conditions imposed on entropy
 * 5) It would be good if the benchmark configuration involved a high compressibility contrast so that the it would test the non-Boussinesq aspect of a code.
 * 6) The benchmark (or one of the benchmark configurations) should test the code on non-stationary problems. Time dependent properties are often much more sensitive to bugs/drawbacks in the code. This would test the time integration scheme too.

[|Gary's suggestions]

Some non-magnetic benchmarks. These come from a purely hydrodynamic code which solves anelastic, rotating, convection in a spherical shell. The code is pseudo-spectral, based on spherical harmonic expansion, with high order finite differences in the radial direction. The equations are formulated using a poloidal-toroidal expansion. The nonlinear code has been tested against an independently constructed linear eigenvalue code. Details are in [|Chris Jones' Hydro Benchmarks]
 * HYDRO BENCHMARKS** (Chris Jones)

**(ASH Code)**
[|ASH_AnelasticFormulation.pdf]

[|First_Order_Anelastic.pdf]
 * THE FIRST ORDER EQUATIONS FOR THE ANELASTIC APPROXIMATION** (Krzysztof Mizerski)

Comparison of Leeds code and ASH code: hopefully useful for running benchmarks with the ASH code [|ASH-Leeds.pdf]

Notes of meeting of 2nd July

First Meeting: Weds 28 May 11:30am: The Tower