Ondřej Chrenko will talk at K4 on Monday April 30, 9:00.

The lecture will end with open problems-tasks for possible cooperation, etc.

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# MathMAC

## Hydrodynamic processes during formation of planetary systems

## Numerical Techniques for Astronomical Explosions

## Hydrodynamic processes during formation of planetary systems

__Abstract__:
## Water generation and transport through the high-pressure ice layers of Ganymede and Titan

## Vědecká stipendia pro studenty PhD. a Mgr.

## High order numerical methods for hyperbolic equations

University center for mathematical modeling, applied analysis and computational mathematics

Ondřej Chrenko will talk at K4 on Monday April 30, 9:00.

The lecture will end with open problems-tasks for possible cooperation, etc.

Dr. Ondřej Pejcha will give a lecture at K4 on Monday April 23, 9:00.

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.

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.

Klára Kalousová is going to give a lecture on *Water generation and transport through the high-pressure ice layers of Ganymede and Titan*. The lecture will take place on Wednesday 7th March at 10:10 in lecture hall T1 (Trója).

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 equationsChi-Wang Shu

Division of Applied Mathematics

Brown University

Providence, RI 02912Hyperbolic 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.