Davide Illiano - Academia.edu (original) (raw)
Papers by Davide Illiano
Numerical simulations and laboratory studies are our main tools to comprehend better processes ha... more Numerical simulations and laboratory studies are our main tools to comprehend better processes happening in the subsurface. The phenomena are modeled thanks to systems of partial differential equations (PDEs), which are extraordinarily complex to solve numerically due to their often highly nonlinear and tightly coupled character. After decades of research on new and improved solving algorithms, there is still a need for accurate and robust schemes. In this work, we investigate linearization schemes and splitting techniques for fully coupled flow and transport in porous media. A particular case of multiphase flow in porous media, the study of water flow in variably saturated porous media, modeled by the Richards equation, is studied here. An external component, e.g., a surfactant, is transported by the water phases. The resulting system of equations is fully coupled and nonlinear. In this work, we investigate three different linearization schemes, the classical Newton method, commonl...
Lecture Notes in Computational Science and Engineering, 2020
In this thesis we compare different iterative approaches for solving the non-linear, coupled mult... more In this thesis we compare different iterative approaches for solving the non-linear, coupled multiphase flow and reactive transport in porous media. Especially, we consider two-phase flow and one a-half phase flow (modeled by Richards equation) coupled with an one component transport equation. Implicit and explicit iterative schemes will be compared in terms of efficiency, robustness and accuracy. The best approach seems to be a fully implicit scheme, which is a slightly modified variant of the classical splitting iterative scheme for coupled equations. We concentrate on three linearization methods: L-scheme, Modified Picard and Newton. We implement them in Matlab and tested on both an academic example, built from a manufactured analytical solution and on a realistic problem, the Salinity Problem. In the first part of the thesis we will also briefly study the generic two-phase flow plus transport equation in porous media, presenting some of the most common solving algorithms such as...
ArXiv, 2020
We study several iterative methods for fully coupled flow and reactive transport in porous media.... more 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 to incorporate nonstandard effects like dynamic capillarity and hysteresis, and a reactive transport equation for the solute. The two model components are strongly coupled. On one hand, the flow affects the concentration of the solute; on the other hand, the surface tension is a function of the solute, which impacts the capillary pressure and, consequently, the flow. After applying an Euler implicit scheme, we consider a set of iterative linearization schemes to solve the resulting nonlinear equations, including both monolithic and two splitting strategies. The latter include a canonical nonlinear splitting and an alternate linearized splitting, which appears to be overall faster in terms of numbers of iterations, based on our numerical studies. T...
In this article, we present new random walk methods to solve flow and transport problems in unsat... more In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the LLL-scheme developed in finite element/volume approaches. The resulting GRW LLL-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW s...
In this paper, we study a model for the transport of an external component, e.g., a surfactant, i... more In this paper, we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin finite elements. The Newton method and the L-Scheme are employed for the linearization and the performance of these schemes is studied numerically. A special focus is set on the effects of dynamic capillarity on the transport equation.
Computational Geosciences
In this work, we consider the transport of a surfactant in variably saturated porous media. The w... more In this work, we consider the transport of a surfactant in variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard, and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence is analyzed. The performance of these schemes is illustrated on five numerical examples. For these examples, the number of iterations and the condition numbers of the linear systems emerging in each iteration are presented.
Numerical simulations and laboratory studies are our main tools to comprehend better processes ha... more Numerical simulations and laboratory studies are our main tools to comprehend better processes happening in the subsurface. The phenomena are modeled thanks to systems of partial differential equations (PDEs), which are extraordinarily complex to solve numerically due to their often highly nonlinear and tightly coupled character. After decades of research on new and improved solving algorithms, there is still a need for accurate and robust schemes. In this work, we investigate linearization schemes and splitting techniques for fully coupled flow and transport in porous media. A particular case of multiphase flow in porous media, the study of water flow in variably saturated porous media, modeled by the Richards equation, is studied here. An external component, e.g., a surfactant, is transported by the water phases. The resulting system of equations is fully coupled and nonlinear. In this work, we investigate three different linearization schemes, the classical Newton method, commonl...
Lecture Notes in Computational Science and Engineering, 2020
In this thesis we compare different iterative approaches for solving the non-linear, coupled mult... more In this thesis we compare different iterative approaches for solving the non-linear, coupled multiphase flow and reactive transport in porous media. Especially, we consider two-phase flow and one a-half phase flow (modeled by Richards equation) coupled with an one component transport equation. Implicit and explicit iterative schemes will be compared in terms of efficiency, robustness and accuracy. The best approach seems to be a fully implicit scheme, which is a slightly modified variant of the classical splitting iterative scheme for coupled equations. We concentrate on three linearization methods: L-scheme, Modified Picard and Newton. We implement them in Matlab and tested on both an academic example, built from a manufactured analytical solution and on a realistic problem, the Salinity Problem. In the first part of the thesis we will also briefly study the generic two-phase flow plus transport equation in porous media, presenting some of the most common solving algorithms such as...
ArXiv, 2020
We study several iterative methods for fully coupled flow and reactive transport in porous media.... more 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 to incorporate nonstandard effects like dynamic capillarity and hysteresis, and a reactive transport equation for the solute. The two model components are strongly coupled. On one hand, the flow affects the concentration of the solute; on the other hand, the surface tension is a function of the solute, which impacts the capillary pressure and, consequently, the flow. After applying an Euler implicit scheme, we consider a set of iterative linearization schemes to solve the resulting nonlinear equations, including both monolithic and two splitting strategies. The latter include a canonical nonlinear splitting and an alternate linearized splitting, which appears to be overall faster in terms of numbers of iterations, based on our numerical studies. T...
In this article, we present new random walk methods to solve flow and transport problems in unsat... more In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the LLL-scheme developed in finite element/volume approaches. The resulting GRW LLL-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW s...
In this paper, we study a model for the transport of an external component, e.g., a surfactant, i... more In this paper, we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin finite elements. The Newton method and the L-Scheme are employed for the linearization and the performance of these schemes is studied numerically. A special focus is set on the effects of dynamic capillarity on the transport equation.
Computational Geosciences
In this work, we consider the transport of a surfactant in variably saturated porous media. The w... more In this work, we consider the transport of a surfactant in variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard, and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence is analyzed. The performance of these schemes is illustrated on five numerical examples. For these examples, the number of iterations and the condition numbers of the linear systems emerging in each iteration are presented.