Related papers: Kinetic Solvers with Adaptive Mesh in Phase Space

Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…

We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…

We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…

A novel coupled level-set lattice Boltzmann method on adaptive Cartesian grids for simulating liquid-gas multiphase flows is presented. The approach addresses the inherent challenges of accurately modeling multiphase systems characterized…

Several approaches are proposed to deal with the problem of the Automatic Schema Matching (ASM). The challenges and difficulties caused by the complexity and uncertainty characterizing both the process and the outcome of Schema Matching…

The parallel solver of the general synthetic iterative scheme (GSIS), as recently developed by Zhang \textit{et. al.} in Comput. Fluids 281 (2024) 106374, is an efficient method to find the solution of the Boltzmann equation…

This paper proposes a topology optimization method for non-thermal and thermal fluid problems using the Lattice Kinetic Scheme (LKS).LKS, which is derived from the Lattice Boltzmann Method (LBM), requires only macroscopic values, such as…

Multiscale non-equilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the…

Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh…

Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel…

We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…

We consider the solution of the fully kinetic (including electrons) Vlasov-Amp\`ere system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian…

We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with…

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use…

Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…

The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…