An adaptive SPH-FVM method with optimized particle-mesh interpolation scheme for strongly compressible multiphase flows

Abstract

Strongly compressible multiphase flows, such as high-pressure bubble pulsations and jets, are typically characterized by complex interfaces with high density ratios, strong discontinuities, and long-term evolutions. As a result, traditional numerical methods often encounter significant challenges, including tracking multiphase interfaces, maintaining accuracy at discontinuous interfaces over long-term simulations, and enforcing physical non-reflection boundary. To address these issues, this paper introduces an adaptive SPH-FVM coupling model that integrates Riemann Smoothed Particle Hydrodynamics (Riemann-SPH) for computations within the core region, and Finite Volume Method (FVM) for calculations in other regions. It retains the benefits of the SPH method in handling large deformations and interface fragmentations, while leveraging the computational efficiency and boundary enforcement capabilities of the FVM method. This model is notably straightforward to implement and fully adaptive following initial setup. The predefined core particle region is adaptively adjusted, leading to a substantial reduction in the number of particles and an enhancement in overall computational efficiency. Furthermore, an optimized particle-mesh interpolation scheme (OPMIS) is proposed to handle the particle-mesh coupling at the interface, effectively mitigating numerical instability when high-pressure waves propagate from particles to meshes in shock problems. Additionally, the model is applied to simulate complex bubble behaviors in both free fields and near-wall boundaries. The numerical accuracy, efficiency, and robustness of the adaptive SPH-FVM model have been rigorously verified.