arXiv subjects

Andrey Gorobets

Publications and source records attributed to Andrey Gorobets.

3 recordsLinked to original sources

arXiv2025

An efficient eigenvalue bounding method: CFL condition revisited

Direct and large-eddy simulations of turbulence are often solved using explicit temporal schemes. However, this imposes very small time-steps because the eigenvalues of the (linearized) dynamical system, re-scaled by the time-step, must lie inside the stability region. In practice, fast and accurate estimations of the spectral radii of both the discrete convective and diffusive terms are therefore needed. This is virtually always done using the so-called CFL condition. On the other hand, the large heterogeneity and complexity of modern supercomputing systems are nowadays hindering the efficient cross-platform portability of CFD codes. In this regard, our leitmotiv reads: relying on a minimal set of (algebraic) kernels is crucial for code portability and maintenance! In this context, this work focuses on the computation of eigenbounds for the above-mentioned convective and diffusive matrices which are needed to determine the time-step \`a la CFL. To do so, a new inexpensive method, that does not require to re-construct these time-dependent matrices, is proposed and tested. It just relies on a sparse-matrix vector product where only vectors change on time. Hence, both implementation in existing codes and cross-platform portability are straightforward. The effectiveness and robustness of the method are demonstrated for different test cases on both structured Cartesian and unstructured meshes. Finally, the method is combined with a self-adaptive temporal scheme, leading to significantly larger time-steps compared with other more conventional CFL-based approaches.

physics.flu-dyn↗

arXiv2025

A rational length scale for large-eddy simulation of turbulence on anisotropic grids

Due to the prohibitive cost of resolving all relevant scales, direct numerical simulations of turbulence remain unfeasible for most real-world applications. Consequently, dynamically simplified formulations are needed for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are widely used both in academia and industry. These models require a subgrid characteristic length, typically linked to the local grid size. While this length scale corresponds to the mesh step for isotropic grids, its definition for unstructured or anisotropic Cartesian meshes, such as the pancake-like meshes commonly used to capture near-wall turbulence or shear layers, remains an open question. Despite its significant influence on LES model performance, no consensus has been reached on its proper formulation. In this work, we introduce a novel subgrid characteristic length. This length scale is derived from the analysis of the entanglement between the numerical discretization and the filtering in LES. Its mathematical properties and simplicity make it a robust choice for reducing the impact of mesh anisotropies on simulation accuracy. The effectiveness of the proposed subgrid length is demonstrated through simulations of decaying isotropic turbulence and a turbulent channel flow using different codes.

physics.flu-dyn↗

arXiv2021

On the implementation of flux limiters in algebraic frameworks

The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are of paramount importance for the temporal integration of high-speed aerodynamics, multiphase flows, and hyperbolic equations in general. Meanwhile, the breakthrough of new computing architectures and the hybridization of supercomputer systems pose a huge portability challenge, particularly for legacy codes, since the computing subroutines that form the algorithms, the so-called kernels, must be adapted to various complex parallel programming paradigms. From this perspective, the development of innovative implementations relying on a minimalist set of kernels simplifies the deployment of scientific computing software on state-of-the-art supercomputers, while it requires the reformulation of algorithms, such as the aforementioned flux limiters. Equipped with basic algebraic topology and graph theory underlying the classical mesh concept, a new flux limiter formulation is presented based on the adoption of algebraic data structures and kernels. As a result, traditional flux limiters are cast into a stream of only two types of computing kernels: sparse matrix-vector multiplication and generalized pointwise binary operators. The newly proposed formulation eases the deployment of such a numerical technique in massively parallel, potentially hybrid, computing systems and is demonstrated for a canonical advection problem.

physics.comp-ph↗