High-resolution transport of regional level sets for evolving complex interface networks
For researchers simulating multi-region flow problems with complex interface topologies, this method offers a more accurate alternative to existing level-set approaches at similar computational cost.
This paper presents a high-resolution transport formulation of the regional level-set method that improves prediction accuracy for complex interface networks while maintaining computational cost comparable to existing methods. The method demonstrates significant accuracy gains across multiple test cases including triple-point advection and dry foam dynamics.
In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local level sets and reconstruction of a global regional level sets, (ii) locally transporting the interface network by employing high-order spatial discretization schemes for improved representation of complex topologies. Various numerical test cases of multi-region flow problems, including triple-point advection, single vortex flow, mean curvature flow, normal driven flow and dry foam dynamics, show that the method is accurate and suitable for a wide range of complex interface-network evolutions. Its overall computational cost is comparable to the Semi-Lagrangian regional level-set method while the prediction accuracy is significantly improved. The approach thus offers a \textbf{viable} alternative to previous interface-network level-set method.