相关论文: A Nonlinear Multigrid Steady-State Solver for Micr…

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hydrodynamic equations, requires significantly more…

One of the central problems in the study of rarefied gas dynamics is to find the steady-state solution of the Boltzmann equation quickly. When the Knudsen number is large, i.e. the system is highly rarefied, the conventional iteration…

In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…

This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a…

The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…

The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…

We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…

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…

We present a geometric multigrid solver for the M1 model of radiative transfer without source terms. In radiative hydrodynamics applications, the radiative transfer needs to be solved implicitly because of the fast propagation speed of…

We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This…

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…

A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better…

The fully implicit method is the most commonly used approach to solve black-oil problems in reservoir simulation. The method requires repeated linearization of large nonlinear systems and produces ill-condi\-tioned linear systems. We…

Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term…

This paper investigates parallelization strategies for solving power flow problems in both transmission and unbalanced, three-phase distribution systems by developing a scalable power flow solver, ExaGridPF, which is compatible with…

We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…