arXiv subjects

Ernesto Pimentel-García

Publications and source records attributed to Ernesto Pimentel-García.

4 recordsLinked to original sources

arXiv2025

High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties, friction and gravity

We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in model parameters are handled using the Generalized Hydrostatic Reconstruction, the presence of algebraic source terms implies that steady state solutions cannot always be computed analytically. In fact, steady states are defined by an ordinary differential equation that needs to be integrated numerically. Therefore, we resort on a numerical reconstruction operator to identify and, where appropriate, preserve steady states with an accuracy that depends on the reconstruction operator's numerical scheme. We extend our methods to deal with networks of vessels and show numerical results for single- and multiple-vessel tests, including a network of 118 vessels, demonstrating the capacity of the presented methods to outperform naive discretizations of the equations under study.

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arXiv2024

High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization

In this work we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented. This extension combined with an in-cell discontinuous reconstruction operator are the key points to develop a new family of high-order methods that are able to capture exactly isolated shocks. Several test cases are proposed to validate these methods for the Modified Shallow Water equations and the Two-Layer Shallow Water system.

math.NA↗

arXiv2021

In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension

We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging topic is presented. This extension is based on the combination of the first-order in-cell reconstruction and the MUSCL-Hancock reconstruction. The first-order strategy allowed in particular to capture exactly the isolated shocks and this new second-order extension keep this property. We also set the basis of an extension to high-order methods following this in-cell methodology and a way for capturing exactly more than one shock. Several numerical tests are proposed to validate the methods for the Coupled-Burgers system, Gas dynamics equations in Lagrangian coordinates and the modified shallow water system.

math.NA↗

arXiv2021

A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background

For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms with first-order or second-order of accuracy. We treat both the relativistic Burgers-Schwarzschild model and the relativistic Euler-Schwarzschild model and take advantage of the explicit or implicit forms available for the stationary solutions of these models. Our schemes follow the finite volume methodology and preserve the stationary solutions. Importantly, they allow us to investigate the global asymptotic behavior of such flows and determine the asymptotic behavior of the mass density and velocity field of the fluid.

math.NA↗