Self Gravity with FFT

Self-Gravity with FFT

A new Gravity class is constructed as a member of MeshBlock. The Gravity class contains the gravitational potential array phi. For the FFT gravity solver, the boundary condition is also separately set for phi (which is unnecessary for the multigrid gravity solver; see Self-Gravity with Multigrid).

When self-gravity is enabled, phi is automatically included in any Outputs that include either the prim or cons variables. Alternatively, it can be explicitly included in the variable field as phi.

A new FFTGravityDriver class is constructed and solves Poisson's equation using FFT assuming periodic BCs in all directions. The FFTGravityDriver::Solve() function is called in the main loop at every time-integrator stage, and it performs the following steps:

1. load density from MeshBlocks to the FFT input array
2. execute forward FFT
3. multiply kernel (-k^-2; SetNormFactor() takes the four_pi_G factor into account)
4. execute backward FFT
5. retrieve the real part of the FFT output, and store in the gravitational potential array phi
6. call gravity tasklist to send/receive boundary values

The momentum source term due to the gravitational force is included in the flux calculation by adding the gravitational tensor. See athena/src/hydro/gravity_fluxes.cpp.

The energy source term due to the gravitational energy flux is separately added as a source term. See athena/src/hydro/srcterm/gravity.cpp.

The gravitational constant (four_pi_G) should be set in Mesh::InitMeshData using SetGravityConstant or SetFourPiG function.

The background mean density (grav_mean_rho) should be set in Mesh::InitMeshData using SetMeanDensity function. For problems with the Jeans' swindle (= fully periodic BCs), this should be the initial mean density (see athena/src/pgen/jeans.cpp; see also #155). For problems with other BCs (not implemented yet), this should be zero.

Since we have switched back to the source term implementation, we do not need to set the mean density any more. A pgen file using SetMeanDensity has to be updated as the function is deleted.

Regression Test (Jeans problem)

> cd tst/regression/
> ./run_tests.py grav

Example

> ./configure.py --prob=poisson -fft --grav=fft
> ./athena -i ../inputs/hydro/athinput.poisson