A basic phenomenon modeled computationally is tracer transport in a flow field, such as in porous medium simulation. We analyze the stability and convergence of a fully conservative characteristic method, the Volume Corrected Characteristics-Mixed Method [4] (VCCMM) applied to advection of a dilute tracer in an incompressible flow. Numerical tests for the optimal convergence rate match the results of our theoretical proof. We avoid the CFL constraint on the time step size and obtain a higher order convergence rate compared with Godunov's method. We describe the implementation of the VCCMM, where we feature and define a polyline class for the volume computation of trace-back regions. Some numerical examples show that large time steps can be used in practice, no overshoot or undershoot arises in the solution, and less numerical diffusion is produced compared with Godunov's method. An application to a nuclear waste disposal problem is also presented, where we simulate the processes of advection, reaction, and diffusion of radioactive elements in a simplified far field model. Finally, an extension of the VCCMM is developed for compressible flows, and a stability and convergence analysis is presented. / text

The exchange of dissolved constituents between a shallow bay and the ocean is governed by regular tidal fluxes as well as by wind generated storm surges and currents. In this study the transport of a conservative tracer was simulated using the numerical model Delft3D in a system of shallow bays along the coast of the Delmarva Peninsula, Virginia. The evaluation of the tracer residence time was carried out using the Eulerian approach. The main mechanisms governing the decay of the tracer concentration inside the lagoons were assessed by considering the influence of different factors such as the time of release of the tracer with respect to the tidal cycle, tidal amplitude, and local winds. The exponential curve well approximates the decay of the tracer concentration in time. A set of simulations shows that the prevailing factor controlling the tracer transport and, therefore, the tracer concentration within the lagoons are wind-driven fluxes. Large tidal amplitudes also promote the flushing of the tracer out of the bay, while the time of tracer release with respect to the tidal phase has been found to play a relatively negligible role. Finally, a simplified approach is presented to compute the decay of tracer concentration in time. The method accounts for hourly variable wind characteristics as well as seasonal changes in meteorological conditions.

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. I describe initial experiments with two independent but complementary strategies for attacking this "time barrier". First I describe computational experiments exploring the performance improvements from overlapping computation and communication on hybrid parallel computers. My test case is explicit time integration of linear advection with constant uniform velocity in a three-dimensional periodic domain. I present results for Fortran implementations using various combinations of MPI, OpenMP, and CUDA, with and without overlap of computation and communication. Second I describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, along with a parallel implementation discretized on the cubed sphere. It shows optimal accuracy at Courant numbers of 10-20, more than an order of magnitude higher than explicit methods. Finally I describe the development and stability analyses of the time integrators and advection methods I used for my experiments. I develop explicit single-step methods with stability up to Courant numbers of one in each dimension, hybrid explicit-implict methods with stability for arbitrary Courant numbers, and interpolation operators that enable the arbitrary stability of semi-Lagrangian methods.

Atrial fibrillation (AF) is the most common arrhythmia that leads to thrombus formation, mostly in the left atrial appendage (LAA). The current standard of stratifying stroke risk, based on the CHA2DS2-VASc score, does not consider LAA morphology, and the clinically accepted LAA morphology-based classification is highly subjective. The aim of this study was to determine whether LAA blood-borne particle residence time distribution and the proposed quantitative index of LAA 3D geometry can add independent information to the CHA2DS2-VASc score. Data were collected from 16 AF subjects. Subject-specific measurements included left atrial (LA) and LAA 3D geometry obtained by cardiac computed tomography, cardiac output, and heart rate.We quantified 3D LAA appearance in terms of a novel LAA appearance complexity index (LAA-ACI). We employed computational fluid dynamics analysis and a systems-based approach to quantify residence time distribution and associated calculated variable (LAA mean residence time, tm) in each subject. The LAA-ACI captured the subject-specific LAA 3D geometry in terms of a single number. LAA tm varied significantly within a given LAA morphology as defined by the current subjectivemethod and it was not simply a reflection of LAA geometry/appearance. In addition, LAA-ACI and LAA tm varied significantly for a given CHA2DS2-VASc score, indicating that these two indices of stasis are not simply a reflection of the subjects’ clinical status. We conclude that LAA-ACI and LAA tm add independent information to the CHA2DS2-VASc score about stasis risk and thereby can potentially enhance its ability to stratify stroke risk in AF patients.

We propose derivations of several models of adsorption-convection-diffusion-type describing  transport in fractured porous media and simulate numerically some of them. As starting point, we consider a basic scenario where the tracer (i.e. the chemical substance of interest) is supposed to cross an heterogeneous porous media made of a regular part and a fissure. The fissure is in our case a straight thin layer fracture. We focus exclusively on reducing the dimension of the fracture to a line, while aiming to derive the correct limit equations and transmission conditions. We employ formal two-scale homogenization asymptotics to derive reduced effective models. The proposed reduced effective models can become useful tools for the engineering community as they can be approximated easily numerically.