Related papers: The Cartesian Grid Active Flux Method with Adaptiv…
A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are…
In this paper, we develop the first entirely graphic processing unit (GPU) based h-adaptive flux reconstruction (FR) method with linear trees. The adaptive solver fully operates on the GPU hardware, using a linear quadtree for two…
We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme…
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…
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…
Interpolating scattered CFD datasets onto a uniform Cartesian grid can distort the true geometry, producing a convex-hull type envelope and activating nonphysical regions. This work presents a reconstruction framework that recovers…
This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx. Therefore, dolfinx_eqlb is introduced, its algorithmic…
The interfacial diffusion associated with finite volume method (FVM) discretizations of multiphase flows creates the need for an interface sharpening mechanism. Such solutions for structured quadrilateral grids are well documented, but…
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
In this paper, a simple field function is presented for facilitating the solution of complex and dynamic fluid-solid systems on Cartesian grids with interface-resolved fluid-fluid, fluid-solid, and solid-solid interactions. For a…
We propose a new discrete FFT-based method for computational homogenization of micromechanics on a regular grid that is simple, fast and robust. The discretization scheme is based on a tetrahedral stencil that displays three crucial…
A protection method in active distribution networks is proposed in this paper. In active distribution systems, fault currents flow in multiple directions and presents a varying range of value, which poses a great challenge of maintaining…
We describe the implementation of multigrid solvers in the Athena++ adaptive mesh refinement (AMR) framework and their application to the solution of the Poisson equation for self-gravity. The new solvers are built on top of the AMR…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
The formation of current sheets in ideal incompressible magnetohydrodynamic flows in two dimensions is studied numerically using the technique of adaptive mesh refinement. The growth of current density is in agreement with simple scaling…
We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive…
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…
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…