Related papers: MP-FVM: Enhancing Finite Volume Method for Water I…
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards' equation reduces to Burgers'…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time…
We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
An analytical solution of the nonlinear Richards equation is presented, for one-dimensional infiltration into a soil of uniform initial moisture content subject to a constant depth of surface ponded water. Adopted mathematical forms of the…
In this study, we derive an analytical solution to address the problem of one-dimensional vertical infiltration within bounded profiles. We consider the Richards equation together with various boundary conditions, simulating different…
The matched interface and boundary (MIB) method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries. However, its collocation formulation…
We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of…
We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the…
Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…
A high-fidelity finite volume scheme based on the BVD (boundary variation diminishing) concept is proposed in this study to solve the ideal magnetohydrodynamics (MHD) equations. A hybrid spatial reconstruction profile, consisting of a…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…