Related papers: Implicit EXP-RBF techniques for modeling unsaturat…
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'…
The importance of accurate soil moisture data for the development of modern closed-loop irrigation systems cannot be overstated. Due to the diversity of soil, it is difficult to obtain an accurate model for agro-hydrological system. In this…
We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…
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…
Semi-analytical multi-front solutions of water table response due to periodic forcing in a partially saturated vertical porous column are developed, tested and compared to finite volume solutions of the Richards equation. The multi-front…
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the…
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
The Position Based Fluids (PBF) method is a state-of-the-art approach for fluid simulations in the context of real-time applications like games. It uses an iterative solver concept that tries to maintain a constant fluid density…
The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model.In most cases, the velocity related to the sediment is much lower that…
We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed…
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in…
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by…
The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with…
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…
Reliability-based design optimization (RBDO) provides a rational and sound framework for finding the optimal design while taking uncertainties into ac-count. The main issue in implementing RBDO methods, particularly stochastic simu-lation…
The study of flow in fractured porous media is a key ingredient for many geoscience applications, such as reservoir management and geothermal energy production. Modelling and simulation of these highly heterogeneous and geometrically…