Related papers: The Riemann problem for a two-phase mixture hyperb…
We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the…
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…
We present a novel approach to kinetic theory modeling enabling the simulation of a generic, real gas presented by its corresponding equation of state. The model is based on mass, momentum and energy conservation, and unlike the lattice…
The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…
We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…
We consider a model of a binary mixture of two immiscible compressible fluids. We propose a numerical scheme and discuss its basic properties: Stability, consistency, convergence. The convergence is established via the method of generalized…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not…
The classical phase-field modeling approaches for multiphase problems represent each phase using a regularized characteristic function, which necessarily introduces a simplex constraint for the phase-field variables. Additionally, the…
We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…
We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find…
In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis…
The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear…
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish…
In the article, correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert method and the Enskog error are considered. The equations system of multi-component nonequilibrium gas-dynamics is derived,…
The objective of this paper is to construct geometrically Riemann $k$-wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equations. To this end, we adapt and combine elements of two…