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In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of…
In this paper we propose a space-time framework for the computation of periodic flows. We employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using…
To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered…
In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods…
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 new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
We establish the existence of Young structures for a broad class of partially hyperbolic diffeomorphisms with a splitting $TM = E^{cs} \oplus E^{uu}$, under exactly the same conditions that ensure the existence of SRB measures in a previous…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…
In this paper, A new sixth-order weighted essentially non-oscillatory (WENO) scheme, refered as the WENO-6, is proposed in the finite volume framework for the hyperbolic conservation laws. Instead of selecting one stencil for each cell in…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
This work presents DCFlow, a novel unsupervised cross-modal flow estimation framework that integrates a decoupled optimization strategy and a cross-modal consistency constraint. Unlike previous approaches that implicitly learn flow…
This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows,…
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed…
In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and their mean value in each triangular element. This type of…