improve energy conservation with gravity about pyro2

[zingale]

this approach is done in Castro now. As pyro is not meant to be a research
code, I opted for simplicity here.

On Mon, Nov 30, 2015 at 9:56 AM, Ben Wibking [email protected]
wrote:

Energy conservation with body forces can be substantially improved if the
mass fluxes are used, instead of the cell-centered estimates of the work.
For general body forces, I have tested:

   energy_update  = 0.5*dtdy*(Flux_y.v(n=self.vars.idens) + Flux_y.jp(1,n=self.vars.idens)) * \
                     0.5*(old_yacc_src.v() + yacc_src.v())*myg.dy

    energy_update += 0.5*dtdx*(Flux_x.v(n=self.vars.idens) + Flux_x.ip(1,n=self.vars.idens)) * \
                     0.5*(old_xacc_src.v() + xacc_src.v())*myg.dx

    ener.v()[:,:] += energy_update

This is identical to the formulation in Springel 2010 (the Arepo paper).

I also switched the half-step prediction using the primitive variables:

V_l[1:,:,vars.iu] += 0.5*dt*0.5*(xacc_src.d[0:-1,:]+xacc_src.d[1:,:])
V_l[1:,:,vars.iv] += 0.5*dt*0.5*(yacc_src.d[0:-1,:]+yacc_src.d[1:,:])

V_r[1:-1,:,vars.iu] += 0.5*dt*0.5*(xacc_src.d[2:,:]+xacc_src.d[1:-1,:])
V_r[1:-1,:,vars.iv] += 0.5*dt*0.5*(yacc_src.d[2:,:]+yacc_src.d[1:-1,:])

``
and likewise for the y-direction. This seems to work well, though there may be a better way to do the indexing for the half-step variables.

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Michael Zingale
Associate Professor

Dept. of Physics & Astronomy • Stony Brook University • Stony Brook, NY
11794-3800
phone: [phone]
e-mail: [email protected]
web: http://www.astro.sunysb.edu/mzingale
github: http://github.com/zingale

[BenWibking]

That is good to know. It is not apparent from the documentation. It is much easier to learn the state-of-the-art techniques if I only have to read through thousands of lines of source code, rather than tens of thousands of lines!