Related papers: Numerical Approximation of Hyperbolic Systems Cont…
We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the…
We present a robust computational framework for the numerical solution of a hyperbolic 6-equation single-velocity two-phase system. The system's main interest is that, when combined with instantaneous mechanical relaxation, it recovers the…
In this work, we propose a new numerical method for the Vlasov-Poisson system that is both asymptotically consistent and stable in the quasineutral regime, i.e. when the Debye length is small compared to the characteristic spatial scale of…
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…
A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an…
A new approach using a hyperbolic-equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional…
In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface…
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate…
We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in $\mathbb R^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We consider models of relativistic matter containing sharp interfaces across which the matter model changes. These models will be relevant for neutron stars with crusts, phase transitions, or for viscous boundaries where the length scale is…
In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…
This paper considers systems of balance law with a dissipative non local source. A global in time well posedness result is obtained. Estimates on the dependence of solutions from the flow and from the source term are also provided. The…
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…
Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…