scholarly journals Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1787 ◽  
Author(s):  
Luka Malenica ◽  
Hrvoje Gotovac ◽  
Grgo Kamber ◽  
Srdjan Simunovic ◽  
Srikanth Allu ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Groundwater Flow ◽  
Physical Model ◽  
Isogeometric Analysis ◽  
Numerical Solutions ◽  
Control Volume ◽  
Karst Aquifers ◽  
Conduit Flow ◽  
Laboratory Conditions

A novel numerical model for groundwater flow in karst aquifers is presented. A discrete-continuum (hybrid) approach, in which a three-dimensional matrix flow is coupled with a one-dimensional conduit flow, was used. The laminar flow in the karst matrix is described by a variably saturated flow equation to account for important hydrodynamic effects in both the saturated and unsaturated zones. Turbulent conduit flow for both free surface and pressurized flow conditions was captured via the noninertia wave equation, whereas the coupling of two flow domains was established through an exchange term proportional to head differences. The novel numerical approach based on Fup basis functions and control-volume formulation enabled us to obtain smooth and locally conservative numerical solutions. Due to its similarity to the isogeometric analysis concept (IGA), we labeled it as control-volume isogeometric analysis (CV-IGA). Since realistic verification of the karst flow models is an extremely difficult task, the particular contribution of this work is the construction of a specially designed 3D physical model ( dimensions: 5.66 × 2.95 × 2.00 m) in order to verify the developed numerical model under controlled laboratory conditions. Heterogeneous porous material was used to simulate the karst matrix, and perforated pipes were used as karst conduits. The model was able to capture many flow characteristics, such as the interaction between the matrix and conduit, rainfall infiltration through the unsaturated zone, direct recharge through sinkholes, and both free surface and pressurized flow in conduits. Two different flow experiments are presented, and comparison with numerical results confirmed the validity of the developed karst flow model under complex laboratory conditions.

scholarly journals Numerical Modeling Based on Spline Basis Functions: Application to Groundwater Flow Modeling in Karst Aquifers and Advection Dominated Problems

2019 ◽  
Author(s):  
◽  
Luka Malenica
Keyword(s):  
Numerical Model ◽  
Groundwater Flow ◽  
Local Time ◽  
Adaptive Algorithm ◽  
Isogeometric Analysis ◽  
Basis Functions ◽  
Spline Functions ◽  
The Novel ◽  
Karst Aquifers ◽  
Spline Basis

The main objective of this thesis is to utilize the powerful approximation properties of spline basis functions for numerical solutions of engineering problems that arise in the field of fluid mechanics. Special types of spline functions, the so-called Fup basis functions, are used as representative members of the spline family. However, the techniques developed in this work are quite general with respect to the choice of different spline functions. The application of this work is twofold. The first practical goal is the development of a novel numerical model for groundwater flow in karst aquifers. The concept of isogeometric analysis (IGA) is presented as a unified framework for multiscale representation of the geometry, material heterogeneity and solution. Moreover, this fundamentally higher-order approach enables the description of all fields as continuous and smooth functions by using a linear combination of spline basis functions. Since classical IGA uses the Galerkin and collocation approach, in this thesis, a third concept, in the form of control volume isogeometric analysis (CV-IGA), is developed and set as the foundation for the development of a karst flow numerical model. A discrete-continuum (hybrid) approach is used, in which a three-dimensional laminar matrix flow is coupled with a one-dimensional turbulent conduit flow. The model is capable of describing variably saturated conditions in both flow domains. Since realistic verification of karst flow models is an extremely difficult task, the particular contribution of this work is the construction of a specially designed 3D physical model (dimensions: 5.66 x 2.95 x 2.00 m) to verify the developed numerical model under controlled laboratory conditions. As a second application, this thesis presents the development of a full space-time adaptive collocation algorithm with particular application to advection-dominated problems. Since these problems are usually characterized by numerical instabilities, the novel adaptive algorithm accurately resolves small-scale features while controlling the numerical error and spurious numerical oscillations without need for any special stabilization technique. The previously developed spatial adaptive strategy dynamically changes the computational grid at each global time step, while the novel adaptive temporal strategy uses different local time steps for different collocation points based on the estimation of the temporal discretization error. Thus, in parts of the domain where temporal changes are demanding, the algorithm uses smaller local time steps, while in other parts, larger local time steps can be used without affecting the overall solution accuracy and stability. In contrast to existing local time stepping methods, the developed method is applicable to implicit discretization and resolves all temporal scales independently of the spatial scales. The efficiency and accuracy of the full space-time adaptive algorithm is verified with some classic 1D and 2D advection-diffusion benchmark test cases.

Adaptive Numerical Modeling of Engineering Problems Using Hierarchical Fup Basis Functions and Control Volume IsoGeometric Analysis

2021 ◽  
Author(s):  
◽  
Grgo Kamber ◽  
Keyword(s):  
Isogeometric Analysis ◽  
Numerical Solutions ◽  
Control Volume ◽  
Spatial Scales ◽  
Basis Functions ◽  
Approximation Properties ◽  
Unified Framework ◽  
B Splines ◽  
Engineering Problems ◽  
Resolution Level

The main objective of this thesis is to utilize the powerful approximation properties of Fup basis functions for numerical solutions of engineering problems with highly localized steep gradients while controlling spurious numerical oscillations and describing different spatial scales. The concept of isogeometric analysis (IGA) is presented as a unified framework for multiscale representation of the geometry and solution. This fundamentally high-order approach enables the description of all fields as continuous and smooth functions by using a linear combination of spline basis functions. Classical IGA usually employs Galerkin or collocation approach using B-splines or NURBS as basis functions. However, in this thesis, a third concept in the form of control volume isogeometric analysis (CV-IGA) is used with Fup basis functions which represent infinitely smooth splines. Novel hierarchical Fup (HF) basis functions is constructed, enabling a local hp-refinement such that they can replace certain basis functions at one resolution level with new basis functions at the next resolution level that have a smaller length of the compact support (h-refinement), but also higher order (p-refinement). This hp-refinement property enables spectral convergence which is significant improvement in comparison to the hierarchical truncated B-splines which enable h-refinement and polynomial convergence. Thus, in domain zones with larger gradients, the algorithm uses smaller local spatial scales, while in other region, larger spatial scales are used, controlling the numerical error by the prescribed accuracy. The efficiency and accuracy of the adaptive algorithm is verified with some classic 1D and 2D benchmark test cases with application to the engineering problems with highly localized steep gradients and advection-dominated problems.

Groundwater flow simulation and its application in GaoSong ore field, China

2018 ◽  
Vol 10 (2) ◽  
pp. 276-284 ◽  
Author(s):  
Gang Chen ◽  
Shiguang Xu ◽  
Chunxue Liu ◽  
Lei Lu ◽  
Liang Guo
Keyword(s):  
Numerical Model ◽  
Flow Field ◽  
Groundwater Flow ◽  
Mine Water ◽  
Permeability Coefficient ◽  
Water Inrush ◽  
Seepage Field ◽  
Groundwater Seepage ◽  
Calculation Results ◽  
Groundwater Flow Field

Abstract Mine water inrush is one of the important factors threatening safe production in mines. The accurate understanding of the mine groundwater flow field can effectively reduce the hazards of mine water inrush. Numerical simulation is an important method to study the groundwater flow field. This paper numerically simulates the groundwater seepage field in the GaoSong ore field. In order to ensure the accuracy of the numerical model, the research team completed 3,724 field fissure measurements in the study area. The fracture measurement results were analyzed using the GEOFRAC method and the whole-area fracture network data were generated. On this basis, the rock mass permeability coefficient tensor of the aquifer in the study area was calculated. The tensor calculation results are used in the numerical model of groundwater flow. After calculation, the obtained numerical model can better represent the groundwater seepage field in the study area. In addition, we designed three different numerical models for calculation, mainly to explore the influence of the tensor assignment of permeability coefficient on the calculation results of water yield of the mine. The results showed that irrational fathom tensor assignment would cause a significant deviation in calculation results.

An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

2021 ◽  
Vol 36 (3) ◽  
pp. 165-176
Author(s):  
Kirill Nikitin ◽  
Yuri Vassilevski ◽  
Ruslan Yanbarisov
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Numerical Results ◽  
Implicit Scheme ◽  
New Approach

Abstract This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Three-dimensional numerical model for open-channels with free-surface variations

2003 ◽  
Vol 41 (1) ◽  
pp. 110-112
Author(s):  
ZhixiaN. Cao ◽  
Rodney Day ◽  
Sarah Liriano
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Three Dimensional ◽  
Open Channels

scholarly journals QUASI TWO-DIMENSIONAL NUMERICAL MODEL FOR FREE-SURFACE-PRESSURIZED FLOWS

2015 ◽  
Vol 71 (4) ◽  
pp. I_571-I_576
Author(s):  
Mirei SHIGE-EDA ◽  
Juichiro AKIYAMA ◽  
Yu KAWAKAMI
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Two Dimensional ◽  
Pressurized Flows
Sign in / Sign up

Export Citation Format

Share Document