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Suggestion of an optimal numerical method for solution of the Rayleigh-Plesset equation with rebounding
Petrík, Peter ; Maršík, František (advisor) ; Zima, Patrik (referee)
Na/ev pram: X a v i l i opt.inia.lm niunericke metody pro le.^ loviuce s pmdkyini kavil acni'mi kolapsx Autor: Peter Peln'k Katedra (usl.av): Malemalickv uslav I ' K Vedouci bakalafske prace: Piol. hit!,. Marsik Fianlisek. UrSc. e-mail vodouci'lio: marsik'nt .ras.c/ Abstrnkt: V praci si ndnicme presnost a casovou miioenosl jednokrokovvch ex- plicit niVh I l i r t u d ( Klin;!,c-l\UtT;i. Bulirscll-St oer) s ;id;ipt a h i l l l l l l l klokem v Kayleijdl- Plesselove lovnici, ktera popiMije vyvoj polomei n pi v nne l)iil)iiii\ \ kapalinr sc /nicnaini tln.ku. McUidv pndcriiujf lok/ilni chybii \ nn.stccli kdlapsu hiihlin. av^ik ^lobi'ilnf c!i\'l)a /usta"\;i \ nidu pou/itc tulcrancc, Bulii'scli-St.ocr inctdda \a ncjiiKMis] CMSOVOH nai'ociK)St. V pfi'padr [^ini^c-Kullii iiK'tnd /;i.\isi \ylicr o|itiiiuil)ii nirtdd\ na pou/itr lolcranci. Pli slrcdnicli tnln ancich ur\'i lilujc \-vpocc! i pnuxiti iT^ukiri/acr. (j. xavcdciii niA'f'1 jicx/ixihlr pmiiirnnr nii'slo rasu. ('MSOV-'I ii/irocno^l poti/,it(' i)nMod\c tiicni' s ruxnynii pou/Jtyini vaiiatil a.nii rovtiicc (i/u(cnuick;i aproxi- inacr/adialiat ick/i aproxiniacc plvniic sln/ky olisa.hu luililiiiy. si lacilt'lun./ nest a.rit.clna kapalina)- I'l'i nekteryeh naslavcniYli \st ilpni'eli paranirl I'll \ i/,ol enilirkc vai'iatile io\"iiice doelii'txi k padu \'ypoelu...
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Matematická analýza a výpočtový algoritmus Rayleighovy-Plessetovy rovnice v okolí prudkého kolapsu bublinky.
Petrík, Peter ; Maršík, František (advisor) ; Rudolf, Pavel (referee)
The Rayleigh-Plesset equation is commonly used to describe the dynamics of spherical bubbles in water. However, as high-speed observations show, the bubble looses its spherical shape during the violent collapse and often ssions into a number of smaller bubbles before it rebounds again or dissolves completely. The objective of the work is to bridge the gap between the \spherical\ Rayleigh-Plesset approach and the \non-spherical\ behavior of the collapsing bubble in conditions when the Rayleigh-Plesset equation is no longer valid. The objective is achieved in 3 steps. First, the new criterion for the assessment of the reliability of the Rayleigh-Plesset equation is proposed. Second, the analysis of the shape stability of the spherical surface of the bubble during the collapse lead to the development of a physical model, which incorporates the loss of shape stability, surface energy dissipation and the ssion process. Moreover it estimates the number of bubble fragments as well as conditions when the ssion occurs. Finally, theoretical results are incorporated into the complex numerical code, with the focus on error estimation, specially propagation of rounding error. The sample numerical results for typical hydrodynamic cavitation situations were calculated. The results of this work have to be further con rmed...
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Matematická analýza a výpočtový algoritmus Rayleighovy-Plessetovy rovnice v okolí prudkého kolapsu bublinky.
Petrík, Peter ; Maršík, František (advisor) ; Rudolf, Pavel (referee)
The Rayleigh-Plesset equation is commonly used to describe the dynamics of spherical bubbles in water. However, as high-speed observations show, the bubble looses its spherical shape during the violent collapse and often ssions into a number of smaller bubbles before it rebounds again or dissolves completely. The objective of the work is to bridge the gap between the \spherical\ Rayleigh-Plesset approach and the \non-spherical\ behavior of the collapsing bubble in conditions when the Rayleigh-Plesset equation is no longer valid. The objective is achieved in 3 steps. First, the new criterion for the assessment of the reliability of the Rayleigh-Plesset equation is proposed. Second, the analysis of the shape stability of the spherical surface of the bubble during the collapse lead to the development of a physical model, which incorporates the loss of shape stability, surface energy dissipation and the ssion process. Moreover it estimates the number of bubble fragments as well as conditions when the ssion occurs. Finally, theoretical results are incorporated into the complex numerical code, with the focus on error estimation, specially propagation of rounding error. The sample numerical results for typical hydrodynamic cavitation situations were calculated. The results of this work have to be further con rmed...
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Suggestion of an optimal numerical method for solution of the Rayleigh-Plesset equation with rebounding
Petrík, Peter ; Zima, Patrik (referee) ; Maršík, František (advisor)
Na/ev pram: X a v i l i opt.inia.lm niunericke metody pro le.^ loviuce s pmdkyini kavil acni'mi kolapsx Autor: Peter Peln'k Katedra (usl.av): Malemalickv uslav I ' K Vedouci bakalafske prace: Piol. hit!,. Marsik Fianlisek. UrSc. e-mail vodouci'lio: marsik'nt .ras.c/ Abstrnkt: V praci si ndnicme presnost a casovou miioenosl jednokrokovvch ex- plicit niVh I l i r t u d ( Klin;!,c-l\UtT;i. Bulirscll-St oer) s ;id;ipt a h i l l l l l l l klokem v Kayleijdl- Plesselove lovnici, ktera popiMije vyvoj polomei n pi v nne l)iil)iiii\ \ kapalinr sc /nicnaini tln.ku. McUidv pndcriiujf lok/ilni chybii \ nn.stccli kdlapsu hiihlin. av^ik ^lobi'ilnf c!i\'l)a /usta"\;i \ nidu pou/itc tulcrancc, Bulii'scli-St.ocr inctdda \a ncjiiKMis] CMSOVOH nai'ociK)St. V pfi'padr [^ini^c-Kullii iiK'tnd /;i.\isi \ylicr o|itiiiuil)ii nirtdd\ na pou/itr lolcranci. Pli slrcdnicli tnln ancich ur\'i lilujc \-vpocc! i pnuxiti iT^ukiri/acr. (j. xavcdciii niA'f'1 jicx/ixihlr pmiiirnnr nii'slo rasu. ('MSOV-'I ii/irocno^l poti/,it(' i)nMod\c tiicni' s ruxnynii pou/Jtyini vaiiatil a.nii rovtiicc (i/u(cnuick;i aproxi- inacr/adialiat ick/i aproxiniacc plvniic sln/ky olisa.hu luililiiiy. si lacilt'lun./ nest a.rit.clna kapalina)- I'l'i nekteryeh naslavcniYli \st ilpni'eli paranirl I'll \ i/,ol enilirkc vai'iatile io\"iiice doelii'txi k padu \'ypoelu...
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