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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Numerical modelling of compressible flow using spectral element method
 Jurček, Martin ; Dolejší, Vít (advisor) ; Kučera, Václav (referee)
The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1
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Spectrum of an operator chracterising the stability of the pipe flow
 Jurček, Martin ; Průša, Vít (advisor) ; Málek, Josef (referee)
Stability is a fundamental property of a solution of a system of differential equations. If the system is represented by a linear differential operator, then the negativity of its spectrum implies the stability of the solution, where the negativ- ity of the spectrum means the absence of eigenvalues with positive real part. The analysis of the spectrum of the corresponding linear operator is used in the study of the stability of the pipe flow. Unlike in other systems, there are no analytic formulas for the eigenvalues of the linearized operator characterizing the stability of the pipe flow and the eigenvalues must be computed numerically. Numerous numerical experiments indicate that the spectrum of the operator is negative, and the pipe flow is stable for all values of the Reynolds number. However, no formal proof of this statement exists so far. The objective of the thesis is to compare the spectrum of the operator characterizing the stability of the pipe flow with the spectrum of a simpler operator for which the analytic formulas for the eigenvalues are available. The comparison of the spectra of the operators might be helpful in formulating conjectures concerning the analytical estimates for the operator characterizing the stability of the pipe flow. 1
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