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We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original…
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutions of multidimensional Euler equations. In this paper we…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is…
The numerical approximation of non-isothermal liquid-vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface…
A modified HLLC-type contact preserving Riemann solver for incompressible two-phase flows using the artificial compressibility formulation is presented. Here, the density is omitted from the pressure evolution equation. Also, while…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in…
In this paper, a second-order generalized Riemann problem (GRP) solver is developed for a two-layer thin film model. Extending the first-order Godunov approach, the solver is used to construct a temporal-spatial coupled second-order…
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…
We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme…
With increasing engineering demands, there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct "physics". There are two families of…
In this paper we establish a new convex integration approach for the barotropic compressible Euler equations in two space dimensions. In contrast to existing literature, our new method generates not only the momentum for given density, but…
We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…
This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D…
The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…
We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows.…
Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor spaces M_i in the presence of a one-component perfect fluid. The…