Adaptive mesh refinement for characteristic codes

with Luis Lehner

The following animations demonstrate a new AMR algorithm designed for characteristic codes. The sample problem is the spherically symmetric Einstein-Klein-Gordon system, using a single ingoing null coordinate v and a compactified radial coordinate x (x=0 is the origin, x=1 is infinity).

Example 1: An imploding massless scalar field pulse from past null infinity, tuned to the near threshold of black hole formation (to within approximately one echo of the critical solution). This example demonstrates the ability of the code to "catch" regions of high truncation error along the ingoing characteristic direction.

The scalar field amplitude phi: phi(x,v) (1.0 MB)
The depth of the hierarchy as a function of v: levels(x,v) (0.7MB)

In both animations above x ranges from [0,0.05], and v is considered time.

Example 2: An initially outgoing massive scalar field pulse in the presence of a black hole (which is excised from the coordinate domain). This example demonstrates the ability of the code to refine along regions of high truncation error along the outgoing characteristic direction (the oscillations are due to interactions with the black hole, and lower frequency components of the field travel slower than higher frequency components because of the mass term ).

The scalar field amplitude phi*r, where r is the areal radius: phi_r(x,v) (3.8 MB)
The depth of the hierarchy as a function of v: levels(x,v) (1.0MB)

In both animations above x ranges from [0,1], and v is considered time.