Clinton P. T. Groth,
Kalvin Tsang,
Jai Sachdev
A Block-Based Parallel Implicit Adaptive Mesh Refinement Algorithm for Compressible Gas Dynamics
A highly parallelized implicit adaptive mesh refinement (AMR)
algorithm will be presented for the system of hyperbolic
partial-differential equations governing steady two-dimensional
inviscid compressible gaseous flows. The AMR algorithm uses a
high-resolution upwind finite-volume spatial discretization procedure
in conjunction with limited linear solution reconstruction and
Riemann-solver based flux functions to solve the governing equations
on multi-block mesh composed of structured curvilinear blocks with
quadrilateral computational cells. A flexible block-based
hierarchical data structure is used to facilitate automatic
solution-directed mesh adaptation according to physics-based
refinement criteria. A matrix-free inexact Newton method is used to
solve the system of nonlinear equations arising from this
finite-volume spatial discretization procedure and a preconditioned
generalized minimal residual (GMRES) method is used to solve the
resulting non-symmetric system of linear equations at each step of the
Newton algorithm. Right preconditioning of linear system is used to
improve performance of the Krylov subspace method. An additive
Schwarz global preconditioner with variable overlap is used in
conjunction with block incomplete LU (BILU) type preconditioners based
on the Jacobian of the first-order upwind scheme for each sub-domain.
The Schwarz preconditioning and block-based data structure readily
allow efficient and scalable parallel implementations of the implicit
AMR approach on distributed-memory multi-processor architectures.
Numerical results will be described for several flow cases,
demonstrating both the effectiveness of the mesh adaptation and
algorithm parallel performance. Parallel implementation, startup
issues, and the influences of overlap and fill level on the
effectiveness of the preconditioning will also be discussed. The
proposed parallel implicit AMR method appears appears to be well
suited for predicting complex flows with disparate spatial and
temporal scales in a reliable and efficient fashion.