Zusammenfassung
We present a numerical method for solving the scalar advection-diffusion
equation using adaptive mesh re- finement. Our solver has three unique
characteristics: (1) it supports arbitrary-order accuracy in space; (2) it
allows different discretizations for the velocity and scalar advected quantity;
and (3) it combines the method of characteristics with an integral equation
formulation. In particular, our solver is based on a second-order accurate,
unconditionally stable, semi-Lagrangian scheme combined with a
spatially-adaptive Chebyshev octree for discretization. We study the
convergence, single-node perfor- mance, strong scaling, and weak scaling of our
scheme for several challenging flows that cannot be resolved efficiently
without using high-order accurate discretizations. For example, we consider
problems for which switching from 4th order to 14th order approximation results
in two orders of magnitude speedups for a fixed accuracy. For our largest run,
we solve a problem with one billion unknowns on a tree with maximum depth equal
to 10 and 14th-order elements on 16,384 cores on the â€STAMPEDE†system at
the Texas Advanced Computing Center.
Nutzer
