On the strong scalability of maritime CFD

Abstract

Since 2004, supercomputer growth has been constrained by energy efficiency rather than raw hardware speeds. To maintain exponential growth of overall computing power, a massive growth in parallelization is under way. To keep up with these changes, computational fluid dynamics (CFD) must improve its strong scalability-its ability to handle lower cells-per-core ratios and achieve finer-grain parallelization. A maritime-focused, unstructured, finite-volume code (ReFRESCO) is used to investigate the scalability problems for incompressible, viscous CFD using two classical test-cases. Existing research suggests that the linear equation-system solver is the main bottleneck to incompressible codes, due to the stiff Poisson pressure equation. Here, these results are expanded by analysing the reasons for this poor scalability. In particular, a number of alternative linear solvers and preconditioners are tested to determine if the scalability problem can be circumvented, including GMRES, Pipelined-GMRES, Flexible-GMRES and BCGS. Conventional block-wise preconditioners are tested, along with multi-grid preconditioners and smoothers in various configurations. Memory-bandwidth constraints and global communication patterns are found to be the main bottleneck, and no stateof-the-art solution techniques which solve the strong-scalability problem satisfactorily could be found. There is significant incentive for more research and development in this area.

A posteriori error and uncertainty estimation in computational ship hydrodynamics

“…Thus, the computational time is expected to be several times that achieved with the standard kω model. That is, albeit the solution of turbulence equations scales better than momentum equations (Hawkes et al, 2018). Although the RST model boasts of modelling turbulent physics more robustly than two-equation models, there are problems in its practical implementation (Parneix et al, 1998).…”

“…Although their focus was predominantly on aerospace applications, several aspects overlap significantly with the field of computational ship hydrodynamics. This prompted Hawkes et al (2018) to address one of the concerns raised by Slotnick et al (2014), specifically, scalability problems of CFD simulations with increasing cell numbers.…”

Chaotic multigrid methods for the solution of elliptic equations

“…Despite these lax convergence tolerances, previous work [7] and other literature [8,9] has shown that repeatedly finding a solution to the linearized pressure equation is a severe bottleneck to the strong scalability of CFD codes. The pressure equation is a stiff, elliptic, Poisson equation which contains many low-frequency error components [10].…”

“…Unfortunately, these methods require global communication patterns which scale very poorly. Efforts to hide or reduce the number of global communications, such as the 'pipelined' version of GMRES (P-GMRES [11]), or improved bi-conjugate gradient methods (IBCGS [12]), provide only minor improvements for parallel CFD [7].…”

“…This is of particular concern where the cells-per-core ratio is low, and the ratio of communications to computations is high. On the coarsest grids of a multigrid solver the cells-per-core ratio is naturally very low, and implicit synchronization of the coarse-grid smoothers limits scalability of multigrid methods [7].…”