Seminar of the “University Center for Mathematical Modeling, Applied Analysis and Computational Mathematics”

The seminar of the “University Center for Mathematical Modeling, Applied Analysis and Computational Mathematics”, that will take place next Wednesday (May 9, 2018) in K2 from 9:00 ’till 10:30. The seminar will consist of short presentations given by master and PhD students supported by the University Center for Mathematical Modeling. The schedule of the talks is given below.

Hydrodynamic processes during formation of planetary systems

The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place next Monday (April 9, 2018) at 9:00 am in K4 .
RNDr. Ondrej Chrenko, Ph.D. will give his first talk of a 3-parter series on Hydrodynamic processes during formation of planetary systems.
Please see the details below.

    Abstract:

Planets form in protoplanetary disks which are rotating structures of gas and dust surrounding young stars. Before a protoplanetary disk disperses, the mass of gas dominates over the mass of solids and thus the evolution of the disk and planets is driven by hydrodynamic phenomena. Although this evolutionary stage does not last longer than several million years, it inevitably predetermines the properties of the emerging planetary system, i.e. the multiplicity of planets, their orbital configuration, distances from the central star, their masses and types (whether they become terrestrial or gas giants). Understanding the impact of hydrodynamic processes on planet formation can help us understand the great diversity among the observed extrasolar planetary systems.

First, I will demonstrate the variety of hydrodynamic processes in protoplanetary disks by reviewing several examples, e.g. instabilities leading to angular momentum transport, instabilities enhancing accretion of solids, and planet-disk interactions leading to planetary migration. Next, I will describe numerical solution of the fluid equations within the framework of so-called FARGO hydrodynamic codes (Masset 2000, Benítez-Llambay & Masset 2016) which are often used to study planet-disk interactions. I will present a recent 2D model focused on interactions of multiple planets with a gas disk and a coupled disk of pebbles (Chrenko et al. 2017). Finally, I will outline a more advanced 3D model which is currently under development and I will discuss the implementation of radiative diffusion and stellar irradiation.

High order numerical methods for hyperbolic equations

The following seminar will be held at the lecture room K4 on Monday, March 26, 2018 at 9:00. Everyone is cordially invited.

High order numerical methods
for hyperbolic equations

Chi-Wang Shu
Division of Applied Mathematics
Brown University
Providence, RI 02912

Hyperbolic equations are used extensively in applications
including fluid dynamics, astrophysics, electro-magnetism,
semi-conductor devices, and biological sciences. High order
accurate numerical methods are efficient for solving such
partial differential equations, however they are difficult
to design because solutions may contain discontinuities.
In this talk we will survey several types of high order
numerical methods for such problems, including weighted
essentially non-oscillatory (WENO) finite difference and
finite volume methods, discontinuous Galerkin finite element
methods, and spectral methods. We will discuss essential
ingredients, properties and relative advantages of each
method, and provide comparisons among these methods. Recent
development and applications of these methods will also be
discussed.