On time integration of groundwater flow equations by spectral methods

1993 ◽  
Vol 29 (4) ◽  
pp. 1257-1267 ◽  
Author(s):  
Giuseppe Gambolati
Keyword(s):  
Groundwater Flow ◽  
Spectral Methods ◽  
Time Integration ◽  
Flow Equations

scholarly journals Comment on “On time integration of ground water flow equations by spectral methods” by G. Gambolati

1994 ◽  
Vol 30 (7) ◽  
pp. 2347-2352 ◽  
Author(s):  
W. Scott Dunbar ◽  
Allan D. Woodbury ◽  
Bahram Nour-Omid
Keyword(s):  
Ground Water ◽  
Water Flow ◽  
Spectral Methods ◽  
Time Integration ◽  
Ground Water Flow ◽  
Flow Equations

A coupled FE model for the joint resolution of the shallow water and the groundwater flow equations

2014 ◽  
Vol 24 (7) ◽  
pp. 1553-1569 ◽  
Author(s):  
H.G. Rábade ◽  
P. Vellando ◽  
F. Padilla ◽  
R. Juncosa
Keyword(s):  
Groundwater Flow ◽  
Shallow Water ◽  
Free Surface Flow ◽  
Element Model ◽  
Surface Flow ◽  
Fe Model ◽  
Content Type ◽  
Flow Equations ◽  
Natural Watersheds ◽  
Joint Resolution

Purpose – A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues. Design/methodology/approach – The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately. Findings – The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature. Originality/value – The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

Groundwater Flow Equations

2017 ◽  
pp. 15-27
Author(s):  
Florimond De Smedt ◽  
Wouter Zijl
Keyword(s):  
Groundwater Flow ◽  
Flow Equations

A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems

2013 ◽  
Vol 13 (5) ◽  
pp. 1408-1431 ◽  
Author(s):  
Samet Y. Kadioglu ◽  
Dana A. Knoll
Keyword(s):  
Incompressible Flow ◽  
Time Integration ◽  
Order Reduction ◽  
Second Order ◽  
Navier Stokes ◽  
Function Evaluation ◽  
Flow Equations ◽  
Flow Problems ◽  
Specific Operator ◽  
Time Accuracy

AbstractWe have introduced a fully second order IMplicit/EXplicit (IMEX) time in-tegration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22,24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations. The IMEX method is applied to the incompressible flow equations in the following manner. The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes. On the other hand, an implicit strategy is employed for the non-hyperbolic terms. The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov (JFNK) method [8,29,31]. This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation. We employ a simple yet quite effective fractional step projection methodology (similar to those in [11,19,21,30]) as our preconditioner inside the JFNK solver. We present results from several test calculations. For each test, we show second order time convergence. Finally, we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.

Semianalytical Time Integration for Transient Groundwater Flow in Confined Aquifers

2007 ◽  
Vol 12 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Guoping Tang ◽  
Akram N. Alshawabkeh ◽  
Dionisio Bernal
Keyword(s):  
Groundwater Flow ◽  
Time Integration ◽  
Confined Aquifers

scholarly journals Groundwater flow equation, overview, derivation, and solution

2021 ◽  
Vol 314 ◽  
pp. 04007
Author(s):  
Lhoussaine El Mezouary ◽  
Bouabid El Mansouri
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Groundwater Flow ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Heat Transfer Equation ◽  
Flow Equations ◽  
Basic Law ◽  
Flow Through ◽  
Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

Robust Implicit Multigrid Reynolds-Stress Model Computation of 3-D Turbomachinery Flows

2006 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Reynolds Stress ◽  
Time Integration ◽  
Computational Cost ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Finite Volume Scheme ◽  
Stress Model ◽  
Mean Flow ◽  
Approximate Factorization ◽  
Flow Equations

The purpose of this paper is to present a numerical methodology for the computation of complex 3-D turbomachinery flows using advanced multiequation turbulence closures, including full 7-equation Reynolds-stress transport models. A general frame-work describing the turbulence models and possible future improvements is presented. The flow equations are discretized on structured multiblock grids, using an upwind biased (O[Δx3] MUSCL reconstruction) finite-volume scheme. Time-integration uses a local-dual-time-stepping implicit procedure, with internal subiterations. Computational efficiency is achieved by a specific approximate factorization of the implicit subiterations, designed to minimize the computational cost of the turbulence-transport-equations. Convergence is still accelerated using a mean-flow-multigrid full-approximation-scheme method, where multigrid is applied on the mean-flow-variables only. Speed-ups of a factor 3 are obtained using 3 levels of multigrid (fine + 2 coarser grids). Computational examples are presented using several Reynolds-stress model variants (and also a baseline k–ε model), for various turbomachinery configurations, and compared with available experimental measurements.

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