Large time asymptotics in contaminant transport in porous media

In this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support. While the main emphasis is on two space dimensions, for the sake of completeness we give a brief summary of the corresponding results for one space dimension. The philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as $t \to \infty$ with numerical solutions of the complete initial value problem. The analytic results are obtained using the method of dominant balance which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit. These are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation. This generates what we call a reduced equation, the solution of which depends crucially on the value of a parameter appearing in the problem. In some cases the reduced equation can be solved explicitly, while others have a particularly intractable structure which inhibits any analytic or numerical progress. However, we can extract a number of global and local properties of the solution, which enables us to form a reasonably complete picture of what the profiles look like. Extensive comparison with numerical solution of the original initial value problem provides convincing confirmation of our analytic solutions. In the final section of the paper, by way of motivation for the work, we give some results concerning the temporal behaviour of certain moments of the two-dimensional profiles commonly used to compute physical parameter characteristics for contaminant transport in porous media

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Novel Loci for Adiponectin Levels and Their Influence on Type 2 Diabetes and Metabolic Traits : A Multi-Ethnic Meta-Analysis of 45,891 Individuals

J. Kaprio, S. Ripatti ja M.-L. Lokki työryhmien jäseniä.Peer reviewe

Limiting profiles in reactive solute transport

Abstract: In this paper we consider the large time structure of reactive solute plumes in two dimensional, macroscopically homogeneous, flow domains. The reactions between the dissolved chemicals and the porous matrix are equilibrium adsorption reactions, given by an isotherm of Freundlich type. We also incorporate the effect of partial and full decay. We use the method of asymptotic balancing to obtain, to leading order, the large time behaviour of the solute concentration and the relevant moments (mass, centre of mass, variance). The method of balancing is based on certain conjectures about the form of the temporal decay and partial spreading of the solute. These conjectures are verified numerically

Large time asymptotics in contaminant transport in porous media

In this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support. While the main emphasis is on two space dimensions, for the sake of completeness we give a brief summary of the corresponding results for one space dimension. The philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as $t \to \infty$ with numerical solutions of the complete initial value problem. The analytic results are obtained using the method of dominant balance which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit. These are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation. This generates what we call a reduced equation, the solution of which depends crucially on the value of a parameter appearing in the problem. In some cases the reduced equation can be solved explicitly, while others have a particularly intractable structure which inhibits any analytic or numerical progress. However, we can extract a number of global and local properties of the solution, which enables us to form a reasonably complete picture of what the profiles look like. Extensive comparison with numerical solution of the original initial value problem provides convincing confirmation of our analytic solutions. In the final section of the paper, by way of motivation for the work, we give some results concerning the temporal behaviour of certain moments of the two-dimensional profiles commonly used to compute physical parameter characteristics for contaminant transport in porous media

Large time profiles in reactive solute transport

In this paper we consider the large time structure of reactive solute plumes in two dimensional, macroscopically homogeneous, flow domains. The reactions between the dissolved chemicals and the porous matrix are equilibrium adsorption reactions, given by an isotherm of Freundlich type. We also incorporate the effect of partial and full decay. We use the method of asymptotic balancing to obtain, to leading order, the large time behaviour of the solute concentration and the relevant moments (mass, centre of mass,variance). The method of balancing is based on certain conjectures about the form of the temporal decay and partial spreading of the solute. These conjectures are verified numerically

Limiting profiles in reactive solute transport

Abstract: In this paper we consider the large time structure of reactive solute plumes in two dimensional, macroscopically homogeneous, flow domains. The reactions between the dissolved chemicals and the porous matrix are equilibrium adsorption reactions, given by an isotherm of Freundlich type. We also incorporate the effect of partial and full decay. We use the method of asymptotic balancing to obtain, to leading order, the large time behaviour of the solute concentration and the relevant moments (mass, centre of mass, variance). The method of balancing is based on certain conjectures about the form of the temporal decay and partial spreading of the solute. These conjectures are verified numerically