arXiv subjects

Eric J. Tovar

Publications and source records attributed to Eric J. Tovar.

5 recordsLinked to original sources

arXiv2026

Well-balanced second-order approximation of the compressible atmospheric Euler equations

We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to rest states. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and typical benchmark problems for atmospheric flows.

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arXiv2026

Invariant-domain preserving IMEX schemes for the nonequilibrium Gray Radiation-Hydrodynamics equations Part I

In this work we introduce an implicit-explicit invariant-domain preserving approximation of the nonequilibrium gray radiation-hydrodynamics equations. A time and space approximation of the system is proposed using a novel split of the equations composed of three elementary subsystems, two hyperbolic and one parabolic. The approximation thus realized is proved to be consistent, conservative, invariant-domain preserving, and first-order accurate. The proposed method is a stepping stone for achieving higher-order accuracy in space and time in the forthcoming second part of this work. The method is numerically illustrated and shown to converge as advertised. This paper is dedicated to the memory of Peter Lax.

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arXiv2025

Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state

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 sufficient wave speed estimate for the Riemann problem under some mild thermodynamic assumptions on the equation of state. This minimum principle is guaranteed through the use of discrete auxiliary states which are in the invariant domain when using this new wave speed estimate. Finally, we numerically illustrate the proposed methodology.

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arXiv2025

Second-order invariant-domain preserving approximation to the multi-species Euler equations

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 to the Riemann problem and derive its maximum wave speed. The maximum wave speed is used in constructing a first-order invariant-domain preserving approximation. We then extend the methodology to second-order accuracy and detail a convex limiting technique which is used for preserving the invariant domain. Finally, the numerical method is verified with analytical solutions and then validated with several benchmarks and laboratory experiments.

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arXiv2022

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

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, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature.

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