Toward asynchronous computations: Proxy equation approach for elliptic systems

Computational solutions of transport equations using traditional schemes scale poorly on massively parallel architectures due to mandatory mathematical synchronization between processing elements (PEs). Asynchronous computations relax the synchronization requirement and scale well on massively parallel architectures but at the cost of reduced accuracy. The proxy equation approach [1] reasonably recovers this loss in accuracy by modifying the flow parameters of the original equation. However, this approach is currently limited to hyperbolic (advection) and parabolic (diffusion) processes. In this study we extend the proxy equation approach to elliptic systems. We utilize pseudo-compressible approach to develop asynchronous schemes for elliptic pressure field in incompressible Navier-Stokes equations. The new scheme is validated using numerical simulations of benchmark problems.

References:

[1] A. Mittal and S. Girimaji, Phys. Rev. E 96, 033304 (2017).