Multi-resolution adaptive modeling of groundwater flow and transport problems

Gotovac, Hrvoje; Andričević, Roko; Gotovac, Blaž

doi:10.1016/j.advwatres.2006.10.007

Cited by 30 publications

(48 citation statements)

References 35 publications

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“…[29] Our recently presented simulation methodology, referred to as Adaptive Fup Monte Carlo Method (AFMCM) [Gotovac et al, 2007[Gotovac et al, , 2009[Gotovac et al, , 2010, supports the Eulerian-Lagrangian formulation and separates the flow from the transport problem. It consists of the following common steps [Rubin, 2003]: (1) generation of logconductivity realizations with predefined correlation structure, (2) numerical approximation of the log-conductivity field, (3) numerical solution of the flow equation with prescribed boundary conditions to produce head and velocity approximations, (4) evaluation of the transport variables for a large number of trajectories, (5) repetition of steps 2-4 for all realizations, and (6) statistical evaluation of transport variables.…”

Section: Flow Simulationsmentioning

confidence: 99%

“…It provides a multiresolution representation of any signal, function or set of data using only a few Fup basis functions and resolution levels on nearly optimal adaptive collocation grids, that are capable of resolving all spatial and/or temporal scales and frequencies. Fup basis functions and the FCT are presented in detail in Gotovac et al [2007]. Other improved Monte Carlo (MC) methodology aspects are: (a) the Fup Regularized Transform (FRT) for data or function (e.g., log-conductivity) approximations in the same multiresolution way as FCT, but computationally more efficient, (b) Adaptive Fup Collocation method (AFCM) for approximation of the flow differential equation, (c) particle tracking algorithm based on the Runge-Kutta-Verner explicit time integration scheme and FRT, and (d) MC statistics represented by Fup basis functions.…”

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

“…Accuracy in the high heterogeneity case is ensured using a recently developed collocation method with Fup basis functions [Gotovac et al, 2007]. We first focus on the statistical nature of the transport resistance b and its dependence on the correlation structure of T, and then seek simple estimators for key statistical properties of b that can be used in applications.…”

Section: Introductionmentioning

confidence: 99%

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Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Cvetković

Gotovac

2013

Water Resources Research

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[1] Diffusive mass transfer in rock fractures is strongly affected by fluid flow in addition to material properties. The flow-dependence of matrix diffusion is quantified by a random variable (''transport resistance'') denoted as b [T/L] and computed from the flow field by following advection trajectories. The numerical methodology for simulating fluid flow is mesh-free, using Fup basis functions. A generic statistical model is used for the transmissivity field, featuring three correlation structures: (i) highly connected non-multiGaussian; (ii) poorly connected (or disconnected) non-multi-Gaussian ; and (iii) multiGaussian. The moments of b are shown to be linear with distance, irrespective of the structure, after approximately 10 integral scales of ln T. Percentiles of b are found to be linear with the mean b when considering all three structures. Taking advantage of this property, a potentially useful relationship is presented between b percentiles and the fracture mean water residence time that integrates all structures with high variability; it can be used in discrete fracture network simulations where T statistical data on individual fractures are not available.Citation: Cvetkovic, V., and H. Gotovac (2013), Flow-dependence of matrix diffusion in highly heterogeneous rock fractures, Water Resour. Res., 49,[7587][7588][7589][7590][7591][7592][7593][7594][7595][7596][7597]

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Section: Flow Simulationsmentioning

confidence: 99%

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Cvetković

Gotovac

2013

Water Resources Research

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“…Fup bazne funkcije ubrajaju se u klasu atomskih baznih funkcija i mogu se definirati kao beskonačno derivabilne krivulje [6]. Rješenja u matrici i kanalu se opisuju umnoškom nepoznatih koeficijenata i baznih funkcija:…”

Section: Numerički Model Tečenja U Kršuunclassified

Physical and numerical flow modeling in karst aquifers

Malenica¹,

Gotovac²,

Kamber³

2017

Zajednički Temelji 2017 - Peti Skup Mladih Istraživača Iz Područja Građevinarstva I Srodnih Tehničkih Znanosti - Zbornik Radova

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SažetakTečenje vode u kršu predstavlja kompleksan hidraulički sustav zbog čega se većina postojećih numeričkih modela bazira na pojednostavljenim matematičkim modelima. U ovom radu se prikazuje razvoj novog numeričkog modela koji bi trebao predstavljati iskorak prema realnijem modeliranju tečenja u kršu. Poseban problem s kompleksnim 3D modelima tečenja u kršu je njihova verifikacija zbog nepoznatih parametara vodonosnika, posebno pozicije, oblika i dimenzija krških kanala. Stoga se u ovom radu prikazuje mogućnost verifikacije numeričkog modela u laboratorijskim uvjetima na posebno izgrađenom fizikalnom modelu krškog vodonosnika. Ključne riječi: krš, tečenje podzemnih voda, fizikalni model, numerički model Physical and numerical flow modeling in karst aquifers AbstractBecause groundwater flow in karst is very complex hydraulic system, most of existing models are based on simplified mathematical models. This work represents attempt toward more reliable modeling of flow in karst. Particular difficulty with complex 3-D karst flow models is its verification due to lack of input data such as parameters of aquifer, especially position, shape and dimensions of conduit network. Therefore, this work shows possibility to verify karst flow models under the laboratory controlled conditions on specially build karst physical model.

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“…Gotovac and Kozulić [8] systemized the existing knowledge on atomic functions and presented the transformation of basis functions into a numerically applicable form. The application of Fup basis functions has been demonstrated in signal processing [14], for solving the integral Fredholm equations [13], in initial value problems [9], and in the collocation methods for boundary value problems [10]. Recently, Fup basis functions were applied to the Monte-Carlo methodology and stochastic processes of flow and transport in heterogeneous porous media [11].…”

Section: Introductionmentioning

confidence: 99%