Venice: a multi-scale operator-splitting algorithm for multi-physics simulations

TL;DR

Venice is a flexible multi-scale operator-splitting algorithm designed for complex multi-physics simulations, enabling dynamic coupling of diverse physical processes across different timescales with improved efficiency.

Contribution

It introduces a novel adaptive operator-splitting method that dynamically couples multi-physics models at various scales, demonstrated through astrophysical simulations.

Findings

Numerical convergence observed with decreasing coupling timescales.

Performance improvements by adjusting coupling timescales.

Successful application to complex astrophysical multi-physics models.

Abstract

We present {\sc Venice}, an operator splitting algorithm to integrate a numerical model on a hierarchy of timescales. {\sc Venice} allows a wide variety of different physical processes operating a different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. The coupling between various physical models and scales is dynamic, and realized through (Strang) operators splitting using adaptive time steps. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how {\sc Venice} can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how {\sc Venice} can be used to gradually build up and tune a complex multi-physics model. Although the examples couple complete numerical models, {\sc Venice} can also be used to efficiently solve systems of stiff differential equations.