相关论文: An asynchronous incomplete block LU preconditioner…
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…
We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive,…
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…
The ILU-based preconditioning methods in previous work have their own parameters to improve their performances. Although the parameters may degrade the performance, their determination is left to users. Thus, these previous methods are not…
A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…
In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a…
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…
In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…
Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier-Stokes model cannot account for both features, and a simple…
Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of the (approximate) Jacobian resulting from linearization of the…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…
We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or…
We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the…
In this paper a new hybrid semi-implicit finite volume / finite element (FV/FE) scheme is presented for the numerical solution of the compressible Euler and Navier-Stokes equations at all Mach numbers on unstructured staggered meshes in two…