Related papers: Development of a Novel Riemann Solver for Solid Dy…
We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant…
Basing on our results [1] on a representation of solutions to the Cauchy problem for multidimensional non-viscous Burgers equation obtained by a method of stochastic perturbation of the associated Langevin system, we deduce an explicit…
This paper presents a novel high-order cell-centered Lagrangian scheme for 2D compressible hydrodynamics by bridging the multi-moment constrained finite volume method (MCV) [16, 51, 52] with a nodal Riemann solver. This scheme (denoted by…
In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order…
Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the…
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and…
A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of…
The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multi-phase flows through different formulations. While already applied to many different configurations in the low Weber and…
This work focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem,…
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-valued fields. The proposed method is convection-semirobust,…
We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the…
Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations…
Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…
A new Riemann solver is built to address numerical resolution of complex flow models. The research direction is closely linked to a variant of the Baer and Nunziato (1986) model developed in Saurel et al. (2017a). This recent model provides…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…