Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting)

This small collaborative workshop brought together experts from the Sino-German project working in the field of advanced numerical methods for hyperbolic balance laws. These are particularly important for compressible fluid flows and related systems of equations. The investigated numerical methods were finite volume/finite difference, discontinuous Galerkin methods, and kinetic-type schemes. We have discussed challenging open mathematical research problems in this field, such as multidimensional shock waves, interfaces with different phases or efficient and problem suited adaptive algorithms. Consequently, our main objective was to discuss novel high-order accurate schemes that reliably approximate underlying physical models and preserve important physically relevant properties. Theoretical questions concerning the convergence of numerical methods and proper solution concepts were addressed as well

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

Multiscale Modeling of Biological Flow using Lattice Boltzmann Method

In this dissertation, we have developed a fluid-structure interaction code specifically designed to simulate soft microparticle deformation in biological flow. We have used this tool for two different applications. First, we study red blood cell deformation under shear flow to evaluate stress distribution on membrane and subsequently pore formation on RBC membrane. Second, we utilized this code to show a proof of concept for an idea where we can separate soft particles based on their biophysical properties. In the following, these applications are discussed in more details.Under high shear rates, pores form on RBC membrane through which hemoglobin leaks out and increases free hemoglobin content of plasma leading to hemolysis. We hypothesize that local flow dynamics such as flow rate and shear stress determines blood cell damage. In this dissertation, a novel model is presented to study red blood cell (RBC) hemolysis at cellular level. The goal of the proposed work is to establish multiscale computational techniques to predict the blood cell dynamics and damage in complex flow conditions, i.e., blood-wetting biomedical devices. The cell membrane damage model will be coupled with local fluid flow to study cell deformation and rupture and a generalized cellular level blood cell damage model will be developed based on these simulations. By coupling Lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single red blood cell under various shear rates. First, we use adaptive meshing to find local strain distribution and critical sites on RBC membrane, then we apply underlying molecular dynamic simulations to evaluate damage. Our approach is comprised of three sub-models: defining criteria of pore formation, calculating pore size, and measuring Hb diffusive flux out of pores. Our damage model uses information of different scales to predict cellular level hemolysis. Results are compared with experimental studies and other models in literature. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.Isolating cells of interest from a heterogeneous mixture has been of critical importance in biological studies and clinical applications. In this dissertation, we have proposed to use ciliary system in microfluidic devices to isolate target subpopulation of soft particles based on their biophysical properties. In this model, the bottom of microchannel is covered with an equally spaced cilia array which can be magnetically actuated. A series of simulations are performed to study cilia-particle interaction and isolation dynamic. It is shown that these elastic hair-like filaments can influence particle’s trajectories differently depending on their biophysical properties. This modeling study also uses immersed boundary (IB) method coupled with lattice Boltzmann method. Soft particles are simulated by connected network of nonlinear springs. Moreover, cilia is modeled by point-particle scheme. It is demonstrated that active ciliary system is able to continuously and non-destructively sort cells based on their size, shape and stiffness. Ultimately, a design map for fabrication of a programmable microfluidic device capable of isolating various subpopulation of cells is developed. This biocompatible, label-free design can separate cells/soft microparticles with high throughput which can greatly complement existing separation technologies

Modeling and simulation in tribology across scales: An overview

This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described