RAUŠ, M. Matematické modelování vln na vodní hladině [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2018.

Posudek vedoucího

Kisela, Tomáš

The thesis deals with modelling of surface water waves near coasts. The topic is quite demanding since the situation is typically described using non-linear partial differential equations. The author managed to combine knowledge and skills in multiple fields such as surface waves theory, theory of PDE, discretization techniques and their implementation. As a result, the thesis contains information from many areas and organizes them into a comprehensible overview with stress put on model Shallow Water Equation and Finite Volume Method. The results are illustrated on several test examples. On the other hand, the thesis contains shortcomings that may have been prevented with a more careful and patient approach. Besides some grammar errors, there is a lack of more detail validation of the results, either with regard to available literature or against some experiment or real situations. The author works with multiple sources which are listed among references, however these sources are referred to in the text only occasionally. In particular, section 2.2 devoted to numerical analysis is poorly referenced to the used literature. I recommend the work for the defense with the grade C.

Posudek oponenta

Štoudková Růžičková, Viera

The goal of the thesis was to propose and in Matlab create a mathematical model of water waves in coastal regions that takes into account the shape of ocean bottom and the velocity of wind. The second chapter of the thesis contains basic concepts. The fluid mechanics parts are the most extensive, but not much used later, in contrast with the mathematics part, which should be more detailed. For example, the notion “hyperbolic” is explained there for a particular system of first order PDE, but it is not labelled as definition and also there is no explanation, what the eigenvalues of the system are. Similarly, “numerical flux” is mentioned in the section (2.2.3), but a vague explanation of this important notion is only in Chapter 5. The next chapter presents three possible mathematical models of ocean waves. It is mentioned there that the first model was derived from the Euler equations, and the other two models were derived from the Navier-Stokes equations. But the Euler equations are not explained or at least mentioned in other parts of this thesis. The Navier-Stokes equations are formulated in the thesis, but with almost no comment on them. In the fourth chapter, the Shallow water equations are derived and analysed. All the steps are thoroughly commented, except of how we get the conservative form (4.24) from (4.23). In the form (4.24) should be „b“, instead of „d“. The Finite volume method is presented in the fifth chapter. Some parts are not very clear. For example, what are the A_s in (5.11) and what are the F_{i+1/2,j}, F_{i-1/2,j} in (5.12)? Further, on p. 49, there is no explanation of the term “ghost cell” and also no reference what the mentioned boundary conditions are. In the whole thesis, they are just described with the words “reflective boundary” and “free boundary” but a definition is missing. The sixth chapter contains the outputs of the Matlab program of the given model, i.e. the height of the water surface at time 0.13 s with various initial and boundary conditions and the velocity of water. The given area is 1x2, the unit is missing. The Matlab code is written clearly, with no significant errors and with thorough comments, but some notions used in them are not explained in the thesis. The thesis contains only reasonable amount of grammatical and typing errors. Its goal has been fulfilled, therefore I recommend the thesis to be defended.

eVSKP id 105807