A Parallel Arbitrary-Order Accurate AMR Algorithm for the Scalar Advection-Diffusion Equation
SessionFluid Dynamics
Session ChairCarol Woodward
Event Type
Paper
Algorithms
Applications
Effective Application of HPC
Intermediate
Introductory
Scientific Computing
TimeWednesday, November 16th2:30pm - 3pm
Location255-EF
DescriptionWe present a novel numerical method to solve the Advection-Diffusion problem. In our approach, we solve the advection equation by using an efficient semi-Lagrangian scheme with multi-algorithmic interpolation. The diffusion equation is solved by applying an integral transform: a convolution with the fundamental solution of the modified Laplace PDE. For time-marching, the Stiffly-Stable method is used. We use a dynamic spatially-adaptive distributed-memory parallelized Chebyshev octree as our data structure. The scheme is arbitrary-order accurate in space and second-order in time. To address load imbalance and communication overhead in distributed-memory Lagrangian schemes, we introduce a novel and robust partitioning scheme. With our scheme, we achieved 50% parallel efficiency for our strong scalability test up to 16k cores on the Stampede at the Texas Advanced Computing Center. Finally, as an application example, we simulate the transport of a substance in a Stokes flow in a porous medium with highly complex pore structure.
