The continuum algorithm: $\mathcal {T}rans$ $\mathcal {F}low$

The continuum algorithm solves the full non-linear, incompressible Navier-Stokes equations in curvilinear coordinates using a control volume formulation. While the details of the numerical method are immaterial to the current project, it is important to summarise a few of the algorithmic features of the solver that are relevant to coupling to the MD code. For example, use of the control volume approach ensure conservation properties are maintained by the solver, and facilitates accurate coupling. The algorithm has been used in prior high-fidelity investigations of stability of shear flows, where accuracy is paramount [13,14]. Also, due to the computational cost, efficient algorithms for the solution of the elliptic pressure equations are required.

This code has been benchmarked on the US Department of Energy (DoE) supercomputers, the supercomputing centre in Germany (HLRB) and, most importantly, on HECToR. As part of the UK-Turbulence Consortium (UKTC), $\mathcal {T}rans$ $\mathcal {F}low$ was verified by Daresbury laboratory for performance and scalability on HECToR. It was also adopted for the most recent massively parallel simulations of turbulent flows on HECToR [7], and demonstrated scalability up to $10^3$ cores.

The parallel implementation of the numerical scheme is via Message Passing Interface (MPI). Domain decomposition is used to divide the solution domain among MPI processes. The choice of the domain size per MPI process is guided by minimising surface area to volume ratio, in order to maximise computations relative to data exchanges. Performance testing was carried out using a Cartesian mesh for turbulent flow over a flat surface. The flow was simulated using $10^6$ grid points per MPI-task. At 1024 cores, the algorithm performed at approximately $90\%$ parallel efficiency relative to the performance on 64 cores.