Related papers: A consistent and conservative volume distribution …
In this paper we validate the implementation of the numerical scheme proposed in [3]. The validation is made by comparison with an explicit solution here obtained, and the solutions of Riemann problems for several networks. We then perform…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
There is a qualitative difference between one-dimensional and multi-dimensional solutions to the Euler equations: new features that arise are vorticity and a nontrivial incompressible (low Mach number) limit. They present challenges to…
Simple modifications for higher-order Godunov-type difference schemes are presented which allow for accurate advection of multi-fluid flows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a…
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…
In the previous work, Zhang et al. proposed a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interactions (FSI) with achieving an optimized computational efficiency meanwhile maintaining good numerical…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving…
The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-stable schemes for this model remains challenging, due to the…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes…
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multicontinuum homogenization, we introduce spatially smooth…
We investigate the mass-preserving $L^2$-gradient flow associated with a generalized Cahn--Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter $\varepsilon > 0$ is small. For well-prepared…
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
We prove existence and regularity for the solutions to a Cahn-Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…