arXiv subjects

A. Klar

Publications and source records attributed to A. Klar.

6 recordsLinked to original sources

arXiv2021

Modeling and simulations of moving droplet in a Rarefied gas

We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In this paper we have excluded the heat transfer between two phases. The interface boundary conditions for the liquid and gas phases is presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction since the droplet moves inside the gas phase and its interface deforms with respect to time and space. Therefore, the similar meshfree particle method is also suitable to solve the incompressible Navier-Stokes equations for liquid phase. To validate the coupled solutions of the BGK model and the incompressible Navier-Stokes equations, we have compared the results of the BGK model and the incompressible Navier-Stokes equations, with those of the Boltzmann and the incompressible Navier-Stokes equations, where the Boltzmann equation is solved by a DSMC method. Results in $1D$ and $2D$ physical spaces are presented.

physics.flu-dyn↗

arXiv2020

Kinetic-controlled hydrodynamics for multilane traffic models

We study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedback control strategies are implemented at the level of vehicles and the aggregate trends are studied by means of Boltzmann-type equations determining three different hydrodynamics based on the lane switching frequency. System of first order macroscopic equations describing the evolution of densities along the lanes are then consistently determined through a suitable closured strategy. Numerical examples are then presented to illustrate the features of the proposed hierarchical approach.

math.OC↗

arXiv2020

Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis

We deduce a model for glioma invasion making use of DTI data and accounting for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment, translated on the one hand into cell stress and corresponding forces and on the other hand into receptor binding dynamics; these lead on the mesoscopic level to kinetic equations involving transport terms w.r.t. all kinetic variables and eventually, by appropriate upscaling, to a macroscopic reaction-diffusion equation for glioma density with multiple taxis, coupled to (integro-)differential equations characterizing the evolution of acidity and macro- and mesoscopic tissue. Our approach also allows for a switch between fast and slower moving regimes, %diffusion- and drift-dominated regimes, according to the local tissue anisotropy. We perform numerical simulations to investigate the behavior of solutions w.r.t. various scenarios of tissue dynamics and the dominance of each of the tactic terms, also suggesting how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. We also provide a discussion about alternative ways of including cell level environmental influences in such multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

q-bio.TO↗

arXiv2018

A meshfree particle method for a vision-based macroscopic pedestrian model

In this paper we present numerical simulations of a macroscopic vision-based model [1] derived from microscopic situation rules described in [2]. This model describes an approach to collision avoidance between pedestrians by taking decisions of turning or slowing down based on basic interaction rules, where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle and of the time-to-interaction. A meshfree particle method is used to solve the equations of the model. Several numerical cases are considered to compare this model with models established in the field, for example, social force model coupled to an Eikonal equation [3]. Particular emphasis is put on the comparison of evacuation and computation times. References 1. Degond P., Appert-Rolland C., Pettere J., Theraulaz G., Vision-based macroscopic pedestrian models, Kinetic and Related models, AIMs 6(4), 809-839 (2013) 2. Ondrej J., Pettere J., Olivier A.H., Donikian S., A synthetic-vision based steering approach for crowd simulation, ACM Transactions on Graphics, 29(4), Article 123 (2010) 3. Etikyala R., Gottlich S., Klar A., Tiwari S., Particle methods for pedestrian flow models: From microscopic to nonlocal continuum models, Mathematical Models and Methods in Applied Sciences, 20(12), 2503-2523 (2014)

math.NA↗

arXiv2016

Experimental Validation of a Microscopic Ellipsoidal Particle Model Immersed in Fluid Flow

A simulation of ellipsoidal particles inside a fluid flow is presented and validated from our own lab size experiments where data has been recorded using a camera set-up and post-processing of the pictures. The model is based on Jeffery's equation, where the orientation and position of the particles are influenced by the surrounding fluid. Additionally, particle-particle interaction and particle-wall interaction are taken into account.

physics.flu-dyn↗

arXiv2014

Single to Double Mill Small Noise Transition via Semi-Lagrangian Finite Volume Methods

We show that double mills are more stable than single mills under stochastic perturbations in swarming dynamic models with basic attraction-repulsion mechanisms. In order to analyse accurately this fact, we will present a numerical technique for solving kinetic mean field equations for swarming dynamics. Numerical solutions of these equations for different sets of parameters will be presented and compared to microscopic and macroscopic results. As a consequence, we numerically observe a phase transition diagram in term of the stochastic noise going from single to double mill for small stochasticity fading gradually to disordered states when the noise strength gets larger. This bifurcation diagram at the inhomogeneous kinetic level is shown by carefully computing the distribution function in velocity space.

math.NA↗