arXiv subjects

Ayoub Gouasmi

Publications and source records attributed to Ayoub Gouasmi.

7 recordsLinked to original sources

arXiv2024

Sparse Data Structures for Efficient State-to-State Kinetic Simulations

Higher-fidelity entry simulations can be enabled by integrating finer thermo-chemistry models into compressible flow physics. One such class of models are State-to-State (StS) kinetics, which explicitly track species populations among quantum energy levels. StS models can represent thermo-chemical non-equilibrium effects that are hardly captured by standard multi-temperature models. However, the associated increase in computational cost is dramatic. For implicit solution techniques that rely on standard block-sparse representations of the Jacobian, both the spatial complexity and the temporal complexity grow quadratically with respect to the number of quantum levels represented. We introduce a more efficient way to represent the Jacobian arising in first-order implicit simulations for compressible flow physics coupled with StS models. The key idea is to recognize that the density of local blocks of the Jacobian comes from rank-one updates that can be managed separately. This leads to a new Jacobian structure, consisting of a fully-sparse matrix and block-wise rank-one updates, whose overall complexity grows linearly with the number of quantum levels. This structure also brings forth a potentially faster variation of the block-Jacobi preconditioning algorithm by leveraging the Sherman-Morrison-Woodbury inversion formula.

physics.comp-ph↗

arXiv2022

Entropy-Stable Schemes in the Low-Mach-Number Regime: Flux-Preconditioning, Entropy Breakdowns, and Entropy Transfers

Entropy-Stable (ES) schemes, specifically those built from [Tadmor \textit{Math. Comput.} 49 (1987) 91], have been gaining interest over the past decade, especially in the context of under-resolved simulations of compressible turbulent flows using high-order methods. These schemes are attractive because they can provide stability in a global and nonlinear sense (consistency with thermodynamics). However, fully realizing the potential of ES schemes requires a better grasp of their local behavior. Entropy-stability itself does not imply good local behavior [Gouasmi \textit{et al.} \textit{J. Sci. Comp.} 78 (2019) 971, Gouasmi \textit{et al.} \textit{Comput. Methd. Appl. M.} 363 (2020) 112912]. In this spirit, we studied ES schemes in problems where \textit{global stability is not the core issue}. In the present work, we consider the accuracy degradation issues typically encountered by upwind-type schemes in the low-Mach-number regime [Turkel \textit{Annu. Rev. Fluid Mech.} 31 (1999) 285] and their treatment using \textit{Flux-Preconditioning} [Turkel \textit{J. Comput. Phys.} 72 (1987) 277, Miczek \textit{et al.} \textit{A \& A} 576 (2015) A50]. ES schemes suffer from the same issues and Flux-Preconditioning can improve their behavior without interfering with entropy-stability. This is first demonstrated analytically: using similarity and congruence transforms we were able to establish conditions for a preconditioned flux to be ES, and introduce the ES variants of the Miczek's and Turkel's preconditioned fluxes. This is then demonstrated numerically through first-order simulations of two simple test problems representative of the incompressible and acoustic limits, the Gresho Vortex and a right-moving acoustic wave. The results are overall consistent with previous studies [...]

physics.flu-dyn↗

arXiv2020

Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations

In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities where the structure required by ES schemes breaks down (the entropy variables are no longer defined). It is shown that while an EC flux is well-defined in this limit, a well-defined upwind ES flux requires appropriately averaged partial densities in the dissipation matrix. A similar result holds for the high-order TecNO reconstruction. However, this does not prevent the numerical solution from developing negative partial densities or internal energy. Numerical experiments were performed on one-dimensional and two-dimensional interface and shock-interface problems. The present scheme exactly preserves stationary interfaces. On moving interfaces, it produces pressure anomalies typically observed with conservative schemes [Karni, \textit{J. Comput. Phys.}, 112 (1994) 1]. We find that these anomalies, which are not present in the single-component case, violate neither entropy stability nor a minimum principle of the specific entropy. Finally, we show that the scheme is able to reproduce the physical mechanisms of the two-dimensional shock-bubble interaction problem [Haas \& Sturtevant, J. Fluid Mech. 181 (1987) 41, Quirk \& Karni, J. Fluid Mech. 318 (1996) 129].

math.NA↗

arXiv2019

A minimum entropy principle in the compressible multicomponent Euler equations

In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1), 1983, pp. 151-164]. This effort allows us to prove a minimum entropy principle on entropy solutions, whether smooth or discrete, in the same way it was originally demonstrated for the compressible Euler equations by [Tadmor, \textit{Appl. Numer. Math.}, 49 (3-5), 1986, pp. 211-219].

math.AP↗

arXiv2018

On entropy stable temporal fluxes

Entropy-stable (ES) schemes have gained considerable attention over the last decade, especially in the context of turbulent flow simulations using high-order methods. While promising because of their nonlinear stability properties, ES schemes have to address a number of issues to become practical. One of them is how much entropy should be produced by the scheme at a certain level of under-resolution. This problem has been so far studied by considering different ES interfaces fluxes in the spatial discretization only because they can be tuned to generate a certain amount of entropy. In this note, we point out that, in the context of space-time discretizations, the same applies to ES interface fluxes in the temporal direction.

math.NA↗

arXiv2018

Entropy Conservative Schemes and the Receding Flow Problem

This work delves into the family of entropy conservative (EC) schemes introduced by Tadmor. The discussion is centered around the Euler equations of fluid mechanics and the receding flow problem extensively studied by Liou. This work is motivated by Liou's recent findings that an abnormal spike in temperature observed with finite-volume schemes is linked to a spurious entropy rise, and that it can be prevented in principle by conserving entropy. While a semi-discrete analysis suggests EC schemes are a good fit, a fully discrete analysis based on Tadmor's framework shows the non-negligible impact of time-integration on the solution behavior. An EC time-integration scheme is developed to show that enforcing conservation of entropy at the fully discrete level does not necessarily guarantee a well-behaved solution.

math.NA↗

arXiv2017

A Priori Estimation Of Memory Effects In Coarse-Grained Nonlinear Systems Using The Mori-Zwanzig Formalism

Reduced Order Models (ROMs) of complex, nonlinear dynamical systems often require closure, which is the process of representing the contribution of the unresolved physics on the resolved physics. The Mori-Zwanzig (M-Z) procedure allows one to write down formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the past history of the resolved variables, and a "noise" term. While the M-Z procedure does not directly reduce the complexity of the original system, these equations can serve as a mathematically consistent starting point to develop closures based on approximations of the memory. In this scenario, a priori knowledge of the memory kernel, which is not explicitly known for nonlinear systems, is of paramount importance to assess the validity of a memory approximation. Unraveling the memory kernel requires the determination of the orthogonal dynamics which is a projected high-dimensional partial differential equation that is not tractable in general. A method to estimate the memory kernel a priori, using full-order solution snapshots, is proposed. The main idea is to solve a pseudo orthogonal dynamics equation, that has a convenient Liouville form, instead of the original one. This ersatz arises from the assumption that the semi-group of the orthogonal dynamics operator is a composition operator, akin to semi-groups of Liouville operators, for one observable. The method is exact in the linear case where the kernel is known explicitly. Results for under-resolved simulations of the Burgers and Kuramoto-Sivashinsky equations demonstrate that the proposed technique can accurately reconstruct the transfer of information between the resolved and unresolved dynamics through memory, and provide valuable information about the kernel.

math.NA↗