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The immersed boundary method (IBM) is widely used in simulating multiphase flows. DCU (Deep Computing Unit) acceleration device is a kind of GPU-like device, which is developed by GPU technology authorised by AMD. To achieve an efficient numerical simulation of two-phase flows, we develop a parallel DCU-based immersed boundary method using the MPI+HIP programming model. To solve the slow convergence problem caused by domain partitioning in multigrid methods, a coarse grid aggregation (CGA) technique is effectively employed. We adopt a nonblocking communication approach with HIP streams to overlap computation and communication. To validate the proposed method running on DCU clusters, we conducted two numerical experiments of droplet deformation in shear flow and the rising bubble. Performance tests show that a speedup of 181 times more than the CPU version can be achieved with 32 DCUs in a $ 1024\times 512\times 512 $ 1024 × 512 × 512 mesh grid. [ABSTRACT FROM AUTHOR]

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier–Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number $ \approx 1 $ ≈ 1), while effectively preserving the mass conservation property. Subsequently, the numerical discretisation of Maxwell's equations under the magnetostatic assumption is described in detail, utilising the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilised for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh–Taylor instability growth in magnetic fluids. [ABSTRACT FROM AUTHOR]

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier–Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position. [ABSTRACT FROM AUTHOR]

In this paper, a kind of arbitrary high order derivatives (ADER) scheme based on the generalised Riemann problem is proposed to simulate multi-material flows by a coupling ghost fluid method. The states at cell interfaces are reconstructed by interpolating polynomials which are piece-wise smooth functions. The states are treated as the equivalent of the left and right states of the Riemann problem. The contact solvers are extrapolated in the vicinity of contact points to facilitate ghost fluids. The numerical method is applied to compressible flows with sharp discontinuities, such as the collision of two fluids of different physical states and gas–liquid two-phase flows. The numerical results demonstrate that unexpected physical oscillations through the contact discontinuities can be prevented effectively and the sharp interface can be captured efficiently. [ABSTRACT FROM AUTHOR]

A mathematical formulation is proposed for the solution of equations governing isentropic gas-liquid flow. The model considered here is a two-fluid model type where the relative velocity between the two phases is implemented by a kinetic constitutive equation. Starting from the conservation of mass and momentum laws, a system of three differential equations is derived in a conservative form for the three principal variables, which are mixture density, mixture velocity and the relative velocity. The governing equations for the mixture offer the novel hyperbolic conservation laws for the description of two-phase flows without any conventional source terms in the momentum or relative velocity equations. The discretisation of the governing equations is based on splitting approach, which is specially designed to allow a straightforward extension to various numerical methods such as Godunov methods of centred-type. To verify the validity of the model, numerical results are presented and discussed. It is demonstrated that the proposed numerical methods have superior overall numerical accuracy among existing methods and models in the literature. The model correctly describes the formation of shocks and rarefactions for the solution of discontinuities in two-phase fluid flow problems, thus verifying the proposed mathematical and numerical investigations. [ABSTRACT FROM AUTHOR]

We describe in this paper, a tool to compute approximate solutions of standard two-fluid models with an equilibrium pressure assumption. The basic approach takes its grounds in the two-fluid two-pressure formalism, and takes advantage of the relaxation techniques. The method may be used to compute either the single- or the two-pressure model, depending on the size of mesh, which is used. It is also shown on the basis of a simple numerical experiment that the local equilibrium assumption may lead to a blow-up of the numerical solution on fine meshes, even if one accounts for drag stabilizing effects. [ABSTRACT FROM AUTHOR]

In this paper, we present the analysis of a full three dimensional transient two-phase flow with strong disequilibria. This analysis uses a finite volume scheme with a recently developed density perturbation method. The application test case is a three dimensional extension of a one-dimensional experiment on blowdown pipe. The results are stable with mesh refinements and show realistic three-dimensional effects. [ABSTRACT FROM AUTHOR]