Implicit-explicit splitting schemes for efficient multiphase flow simulation

• Applicant: Douglas Ramalho Queiroz Pacheco, Ph.D.
• Subject Area: Fluid Mechanics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 580712987

Multiphase systems, whether separated (e.g., water-oil) or dispersed (e.g., ash-air), arise in most natural and industrial processes. Simulating such flows is both economically and environmentally important, yet often complex and costly. This project aims to advance numerical methods for challenging multiphase flows by developing a new class of IMplicit–EXplicit (IMEX) algorithms that unify interface-capturing and Euler–Euler approaches. Despite the strong physical coupling between phases, we focus on carefully designed time discretisations that selectively treat certain terms explicitly through accurate time-lagging. This strategy decouples individual phase subproblems, minimising computational overhead while maintaining the physical consistency demanded by challenging applications such as dam breaks or granular flows. A key objective is to achieve second-order accuracy and unconditional stability in time without resorting to costly nonlinear coupling at each time step. By extrapolating pressure and interphase drag terms, our schemes uphold mathematical rigour while improving computational efficiency. Notably, combining second-order accuracy with unconditional stability enables the use of larger time steps, thereby directly reducing simulation costs. Moreover, our time-stepping methods are designed to be spatial-discretisation-agnostic, meaning they can be combined with finite volumes, finite elements, or other frameworks. Although motivated by challenging applications and models, this project focuses primarily on numerical developments. To ground our work in realistic conditions, we will test and demonstrate our methods on representative flows, including volcanic ash dynamics in collaboration with the Geological and Mining Institute of Spain. Rather than validating or introducing physical models, we adopt well-established multiphase equations and use real data primarily to identify potential numerical issues and to refine the numerical design. Where needed, we incorporate stabilisation techniques (e.g., variational multiscale methods, bound-preserving transport) to address issues such as convection dominance and to enforce physically meaningful volume-fraction constraints. Ultimately, this project seeks to bridge a gap between highly specialised solvers for specific flow regimes and the need for a unified, broadly applicable framework capable of addressing both sharp interfaces and dispersed phases with equal rigour, robustness, and efficiency. By providing a second-order, stable, decoupled framework—together with theoretical analysis, demonstrative benchmarks, and real-data exploration—we aim to significantly broaden the accessibility of advanced multiphase simulations. Our results will reach the community through publications in established engineering and CFD journals as well as presentations at international conferences, ensuring that researchers and practitioners can adopt, further develop, and benefit from these novel IMEX methods.

• DFG Programme: Research Grants