Multi-Solver Coupling for Parallel Adaptive Multi-Physics Simulations with Trixi$.$jl and deal$.$II

2026-07-28

AI Summary

This work addresses the challenge that existing frameworks struggle to efficiently support the direct development of multiphysics coupling solvers and parallel adaptive simulations. We propose a portable, reproducible cross-language framework that, for the first time, tightly integrates Trixi.jl with deal.II to construct a strongly coupled partitioned solver for Newtonian self-gravitating hydrodynamics. By combining a strong coupling strategy, cross-language interoperability, adaptive mesh refinement, and parallel computing, our framework substantially simplifies the development of coupled solvers. Numerical experiments demonstrate high-order convergence, physical consistency, and effective adaptivity of the algorithm, while also exhibiting favorable strong scaling performance in parallel execution.

Abstract

Many standalone frameworks for numerical solvers have been developed to tackle the simulation of specific single- or multi-physics problems. For solving coupled problems, common approaches are to extend existing solvers, to develop an entirely new solver or to couple two existing solvers by using the interface provided by a coupling library or framework. However, to the best of our knowledge, there is not yet a framework that allows the easy and direct development of coupled solvers. In this work, we prototype a portable reproducible cross-language framework for the development of coupled parallel adaptive solvers using Trixi$.$jl and deal$.$II for the numerical simulation of coupled multi-physics problems. Currently, this is tightly entangled with an example coupled solver. We show its usability by developing a partitioned strongly-coupled multi-physics solver for the dynamics of Newtonian self-gravitational gases. For the coupled solver, we validate the expected order of convergence, physical sensibility of the results and mesh adaptivity. Finally, we investigate its parallel scaling. A publicly accessible reproducibility repository for the numerical results and code is available.

Problem

• coupled solvers
• multi-physics simulations
• parallel adaptive
• numerical framework
• solver coupling

Innovation

• multi-solver coupling
• cross-language framework
• parallel adaptive simulation
• strongly-coupled multi-physics
• reproducible research