Related papers: Revisiting the method of characteristics via a con…
This article examines the use of characteristic methods in stratified two-phase pipe flow simulations for obtaining non-dissipative flow predictions. A Roe scheme and several methods based on the principle of characteristics are presented…
We consider an obstacle problem for (possibly non-local) wave equations, and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme. We provide the corresponding numerical…
The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified…
Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
The shear shallow water model provides an approximation for shallow water flows by including the effect of vertical shear in the model. This model can be derived from the depth averaging process by including the second order velocity…
The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a…
The entropy conservative, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernandez et al. (2019), is extended from the compressible Euler equations to the compressible Navier-Stokes equations.…
A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the unsteady case. Central to the framework is an optimization…
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…
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar…
We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and…
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in this setting that apply to piecewise smooth entropy…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solutions are not unique and can be viewed as inviscid limits of…
In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum…
We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while…