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A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS)…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for…
For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…
In this paper, two mesh-free CFD solvers for pore-scale fluid flow through porous media are considered, namely the Lattice Boltzmann Method with the two relaxation time collision term and the direct Navier-Stokes solver under the artificial…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime…
The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…