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Riemann problems at geometric discontinuities are a classic and fascinating issue of hydraulics. In the present paper, the complete solution to the Riemann problem of the one-dimensional Shallow water Equations at monotonic width…
In this paper, we consider Riemann solvers with phase transition effects based on the Euler-Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition…
This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Gamma -1)rho. Here we present the equations of motion and describe a computer code capable of simulating…
We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for the Euler equations for potential flow. With the introduction of three critical angles: the…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is…
Porosity-based models are a viable alternative to classical two-dimensional (2-d) Shallow water Equations (SWE) when the interaction of shallow flows with obstacles is modelled. The exact solution of the Single Porosity (SP) Riemann…
We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous…
This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear…
We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, gfs.sourceforge.net) we compute solutions of the bubble dynamics (i.e. shape and…
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…
Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based…
Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 x 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…
Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a…