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Discontinuous Galerkin Methods for Solving Acoustic Problems
Nytra, Jan ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
Partial differential equations play an important role in engineering applications. It is often possible to solve these equations only approximately, i.e. numerically. Therefore number of successful discretization techniques has been developed to solve these equations. The presented discontinuous Galerkin method seems to be very general method to solve this type of equations, especially useful for hyperbolic systems. Our aim is to solve aeroacoustic problems, where propagation of acoustic waves is described using linearized Euler equations. This system of equations is indeed hyperbolic and therefore the discontinuous Galerkin method was chosen. The most important aspects of this method is ability to deal with complex geometries, possibility of high-order method and its local character enabling efficient computation parallelization. We first introduce the discontinuous Galerkin method in general for one- and two-dimensional problems. We then test the algorithm to solve advection equation, which was chosen as a model case of hyperbolic equation. The method will be finally tested using number of verification problems, which were formulated to test methods for computational equations, including verification of boundary conditions, which, similarly to computational fluid dynamics, are important part of computational aeroacoustics.
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Meshfree methods for computational aeroacoustics
Bajko, Jaroslav ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
Meshfree methods represent an alternative to the standard mesh-based numerical discretization techniques. Considerable effort has been spent on the verification of the meshless methods capabilities to solve problems from different engineering branches in the past decades. The aim of this master's thesis is an application of a suitable meshfree method in the computational aeroacoustics. Main attention will be focused on the sound propagation problems, which can be modeled using the linearized Euler equations. Necessary theory of the hyperbolic systems will be mentioned with respect to the nature of governing equations. Meshfree Finite point method (FPM) has been chosen due to its achievements in the computational fluid dynamics. The derivation of this meshfree method is presented as well as an accuracy improvements which are necessary for the sound propagation problems. Capabilities of the derived meshfree method will be verified on several benchmark problems using a software which was specially developed for this purpose.
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Discontinuous Galerkin Methods for Solving Acoustic Problems
Nytra, Jan ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
Partial differential equations play an important role in engineering applications. It is often possible to solve these equations only approximately, i.e. numerically. Therefore number of successful discretization techniques has been developed to solve these equations. The presented discontinuous Galerkin method seems to be very general method to solve this type of equations, especially useful for hyperbolic systems. Our aim is to solve aeroacoustic problems, where propagation of acoustic waves is described using linearized Euler equations. This system of equations is indeed hyperbolic and therefore the discontinuous Galerkin method was chosen. The most important aspects of this method is ability to deal with complex geometries, possibility of high-order method and its local character enabling efficient computation parallelization. We first introduce the discontinuous Galerkin method in general for one- and two-dimensional problems. We then test the algorithm to solve advection equation, which was chosen as a model case of hyperbolic equation. The method will be finally tested using number of verification problems, which were formulated to test methods for computational equations, including verification of boundary conditions, which, similarly to computational fluid dynamics, are important part of computational aeroacoustics.
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Meshfree methods for computational aeroacoustics
Bajko, Jaroslav ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
Meshfree methods represent an alternative to the standard mesh-based numerical discretization techniques. Considerable effort has been spent on the verification of the meshless methods capabilities to solve problems from different engineering branches in the past decades. The aim of this master's thesis is an application of a suitable meshfree method in the computational aeroacoustics. Main attention will be focused on the sound propagation problems, which can be modeled using the linearized Euler equations. Necessary theory of the hyperbolic systems will be mentioned with respect to the nature of governing equations. Meshfree Finite point method (FPM) has been chosen due to its achievements in the computational fluid dynamics. The derivation of this meshfree method is presented as well as an accuracy improvements which are necessary for the sound propagation problems. Capabilities of the derived meshfree method will be verified on several benchmark problems using a software which was specially developed for this purpose.
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