arXiv subjects

Domenico Caparello

Publications and source records attributed to Domenico Caparello.

4 recordsLinked to original sources

arXiv2026

An IMEX multi-level domain-decomposition method for the Boltzmann equation on unstructured meshes

We introduce a dynamically adaptive multi-level method for the multiscale Boltzmann equation on unstructured meshes, coupling the compressible Euler, Navier-Stokes, and full Boltzmann descriptions within a single asymptotic-preserving IMEX framework. Unlike standard domain-decomposition approaches, where independent solvers exchange data only through interface conditions, the three models form a unified multiregime scheme. They share the same globally stiffly accurate IMEX Runge-Kutta discretization and are synchronized at every internal stage through kinetic-to-fluid moment projections and fluid-to-kinetic lifting. This stage-wise coupling maintains temporal consistency across model interfaces, while the asymptotic-preserving structure ensures compatibility with the fluid limit as the Knudsen number becomes small. The active description is selected in each cell through moment-realizability indicators derived from successive Chapman-Enskog approximations. The hierarchy uses Euler in near-equilibrium regions, Navier-Stokes where first-order nonequilibrium corrections are sufficient, and the full Boltzmann equation where a kinetic description is required. Using Navier-Stokes as the intermediate level avoids evolving a velocity distribution in mildly nonequilibrium regions, which is particularly advantageous on unstructured meshes, where kinetic transport dominates the cost. The spatial discretization combines finite-volume WENO reconstruction on triangular meshes with a conservative fast spectral method for the Boltzmann collision operator. Numerical experiments show that the method closely reproduces the full Boltzmann reference while significantly reducing the computational cost. These results suggest that tightly coupled AP model hierarchies are a viable alternative to interface-based domain decomposition for deterministic kinetic simulations in complex geometries.

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arXiv2025

A Coupled IMEX Domain Decomposition Method for High-Order Time Integration of the ES-BGK Model of the Boltzmann Equation

In this paper, we propose a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, which dynamically detects regions of equilibrium and non-equilibrium. Our implementation automatically switches between Euler equations in regions where the fluid is at equilibrium, and the ES-BGK model elsewhere. The main challenge addressed in this work is the development of a coupled strategy between the macroscopic and the kinetic solvers, which preserves the overall temporal order of accuracy of the scheme. A coupled IMEX method is introduced across decomposed subdomains and solvers. This approach is based on a coupled IMEX method and allows high accuracy and computational efficiency. Several numerical simulations in two space dimensions are performed, in order to validate the robustness of our approach and the expected temporal high-order convergence.

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arXiv2025

High-Order Asymptotic-Preserving IMEX schemes for an ES-BGK model for Gas Mixtures

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy proposed in [Filbet, Jin, J. Sci. Comput., 2011] for the single-species BGK model and is here extended to the multi-species ES-BGK setting. The resulting method is fully explicit, uniformly stable with respect to the Knudsen number and, in the fluid regime, it reduces to a consistent and high-order accurate solver for the limiting macroscopic equations of the mixture. The IMEX structure removes the stiffness associated with the relaxation term so that the time step is constrained only by a hyperbolic CFL condition. The full solver couples a high-order space and velocity discretization that includes third-order time integration, a CWENO3 finite-volume reconstruction in space, exact conservation of macroscopic moments in the discrete velocity space, and a multithreaded implementation. The proposed approach can handle an arbitrary number of species. Its accuracy and robustness are demonstrated on a set of multidimensional kinetic tests for gas mixtures, where the AP property and the correct asymptotics are numerically verified across different regimes.

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arXiv2025

Hierarchical dynamic domain decomposition for the multiscale Boltzmann equation

In this work, we present a hierarchical domain decomposition method for the multi-scale Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in \cite{lev-mor-nad-1998}. This criterion is used to dynamically partition the two-dimensional spatial domain into three regimes: the Euler regime, an intermediate kinetic regime governed by the ES-BGK model, and the full Boltzmann regime. The key advantage of this approach lies in the use of Euler equations in regions where the flow is near hydrodynamic equilibrium, the ES-BGK model in moderately non-equilibrium regions where a fluid description is insufficient but full kinetic resolution is not yet necessary, and the full Boltzmann solver where strong non-equilibrium effects dominate, such as near shocks and boundary layers. This allows for both high accuracy and significant computational savings, as the Euler solver and the ES-BGK models are considerably cheaper than the full kinetic Boltzmann model. To ensure accurate and efficient coupling between regimes, we employ asymptotic-preserving (AP) numerical schemes and fast spectral solvers for evaluating the Boltzmann collision operator. Among the main novelties of this work are the use of a full 2D spatial and 3D velocity decomposition, the integration of three distinct physical regimes within a unified solver framework, and a parallelized implementation exploiting CPU multithreading. This combination enables robust and scalable simulation of multiscale kinetic flows with complex geometries.

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