numerical methods

Mini Course Part 2-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

-

B1 L3 R3119

In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

Mini Course Part 3-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

-

B1 L3 R3119

In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

Mini Course Part 1-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

-

B1 L3 R3119

In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

Deterministic particle approximation for nonlinear transport equations

-

Building L3 R3119

Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.