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The accuracy of Lagrangian point-particle models for simulation of particle-laden flows may degrade when the particle and fluid momentum equations are two-way coupled. In these cases the fluid velocity at the location of the particle, which…

An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…

Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Non divergence-free discretisations for the incompressible Stokes problem may suffer from a lack of pressure-robustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that…

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…

We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume…

The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$\omega$ model designed for efficient Graphics Processing Unit (GPU) execution. The…

We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…

We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…

We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an…

An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g.,…