Eric Tovar
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View article: A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement
A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement Open
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 sui…
View article: Second-order invariant-domain preserving approximation to the multi-species Euler equations
Second-order invariant-domain preserving approximation to the multi-species Euler equations Open
This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled by an ideal gas equation of state. We give the full solution…
View article: Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state
Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state Open
This paper is concerned with constructing an invariant-domain preserving approximation technique for the compressible Euler equations with general equations of state that preserves the minimum principle on the physical entropy. We derive a…
View article: A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations
A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations Open
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 explici…
View article: Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state Open
This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, inva…
View article: Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography
Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography Open
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. an…
View article: Hyperbolic relaxation technique for solving the dispersive Serre Equations with topography.
Hyperbolic relaxation technique for solving the dispersive Serre Equations with topography. Open
The objective of this note is to propose a relaxation technique that accounts for the topography effects in the dispersive Serre equations (also known as Serre--Green--Naghdi or fully non-linear Boussinesq equations, etc.) introduced in [t…
View article: On Peakon and Kink-peakon Solutions to a (2 + 1) Dimensional Generalized Camassa-Holm Equation
On Peakon and Kink-peakon Solutions to a (2 + 1) Dimensional Generalized Camassa-Holm Equation Open
In this paper, we study a (2 + 1)-dimensional generalized Camassa-Holm (2dgCH) equation with both quadratic and cubic nonlinearity. We derive a peaked soliton (peakon) solution, double-peakon solutions, and kink-peakon solutions. In partic…