arXiv subjects

Eric Tovar

Publications and source records attributed to Eric Tovar.

3 recordsLinked to original sources

arXiv2025

A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement

We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with suitable refinement indicators, the proposed scheme enables a provably IDP adaptive numerical method for hyperbolic systems where preservation of physical properties is essential. In addition to proofs of these characteristics, we supply a detailed construction of the method in the context of a high-performance finite element code. To illustrate our proposed scheme, we study a suite of computationally challenging benchmark problems, demonstrating enhanced accuracy and efficiency properties while entirely avoiding \emph{ad hoc} corrections to preserve physical invariants.

math.NA↗

arXiv2024

A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations

We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest states. The employed time-stepping technique is a novel explicit Runge-Kutta (ERK) approach which is an extension of the class of ERK-IDP methods introduced by Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366--A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

math.NA↗

arXiv2021

Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography

The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as the fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) and Seabra-Santos el al (J. Fluid Mec.h, 176, 117-134, 1997). This is done by revisiting a similar relaxation technique introduced in Guermond el al (J. Comput. Phys., 399, 108917, 2019) with partial topography effects. We also derive a family of analytical solutions for the one-dimensional dispersive Serre-Green-Naghdi equations that are used to verify the correctness the proposed relaxed model. The method is then numerically illustrated and validated by comparison with experimental results.

math.NA↗