Dissipation

Erik Schnetter <schnetter@aei.mpg.de>, Bernard Kelly <bernard.j.kelly@nasa.gov>

Date

Abstract

Add nth-order Kreiss-Oliger dissipation to the right hand side of evolution equations. This thorn is intended for time evolutions that use MoL.

1 Physical System

For a description of Kreiss-Oliger artificial dissipation, see [1].

The additional dissipation terms appear as follows, for a general grid function U. Here, the tensor character of the field is irrelevant: each component of, say, γ̃ij is treated as an independent field for dissipation purposes.

tU = tU + (1)(p+3)2𝜖 1 2p+1 hxp (p+1) x(p+1) + hyp (p+1) y(p+1) + hzp (p+1) z(p+1) U, = tU + (1)(p+3)2𝜖 hp 2p+1 (p+1) x(p+1) + (p+1) y(p+1) + (p+1) z(p+1) U,

where hx, hy, and hz are the local grid spacings in each Cartesian direction, and the second equality holds in the usual situation where the three are equal: hx = hy = hz = h.

2 Implementation in Cactus

The Dissipation thorn’s dissipation rate is controlled by a small number of parameters:

Currently available values of order are p {1,3,5,7,9}. To apply dissipation at order p requires that we have at least (p + 1)2 ghostzones — {1,2,3,4,5}, respectively.

The list of fields to be dissipated is specified in the parameter vars. The thorn does not allow