Related papers: Model adaptation for hyperbolic balance laws
We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…
This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…
A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate. We prove the local exact one-sided boundary null controllability of…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh,…
Continual learning has traditionally focused on classifying either instances or classes, but real-world applications, such as robotics and self-driving cars, require models to handle both simultaneously. To mirror real-life scenarios, we…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws…
Stabilization of partial differential equations is a topic of utmost importance in mathematics as well as in engineering sciences. Concerning one dimensional problems there exists a well developed theory. Due to numerous important…
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…