رسالة جامعية
Some numerical and analytical methods for equations of wave propagation and kinetic theory
| العنوان: | Some numerical and analytical methods for equations of wave propagation and kinetic theory |
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| المؤلفون: | Mossberg, Eva |
| بيانات النشر: | Karlstads universitet, Avdelningen för matematik; Karlstad, 2008. |
| سنة النشر: | 2008 |
| المجموعة: | DiVA Archive at Upsalla University |
| Original Material: | urn:isbn:978-91-7063-192-4 |
| مصطلحات موضوعية: | wave propagation, finite difference metods high order methods, Landau-Fokker-Planck equation, Monte-Carlo simulations, Boltzmann equation, hard sphere model, eigenvalue problem, MATHEMATICS, MATEMATIK |
| الوصف: | This thesis consists of two different parts, related to two different fields in mathematical physics: wave propagation and kinetic theory of gases. Various mathematical and computational problems for equations from these areas are treated. The first part is devoted to high order finite difference methods for the Helmholtz equation and the wave equation. Compact schemes with high order accuracy are obtained from an investigation of the function derivatives in the truncation error. With the help of the equation itself, it is possible to transfer high order derivatives to lower order or to transfer time derivatives to space derivatives. For the Helmholtz equation, a compact scheme based on this principle is compared to standard schemes and to deferred correction schemes, and the characteristics of the errors for the different methods are demonstrated and discussed. For the wave equation, a finite difference scheme with fourth order accuracy in both space and time is constructed and applied to a problem in discontinuous media. The second part addresses some problems related to kinetic equations. A direct simulation Monte-Carlo method is constructed for the Landau-Fokker-Planck equation, and numerical tests are performed to verify the accuracy of the algorithm. A formal derivation of the method from the Boltzmann equation with grazing collisions is performed. The linear and linearized Boltzmann collision operators for the hard sphere molecular model are studied using exact reduction of integral equations to ordinary differential equations. It is demonstrated how the eigenvalues of the operators are found from these equations, and numerical values are computed. A proof of existence of non-zero discrete eigenvalues is given. The ordinary diffential equations are also used for investigation of the Chapman-Enskog distribution function with respect to its asymptotic behavior. |
| Original Identifier: | oai:DiVA.org:kau-1848 |
| نوع الوثيقة: | Doctoral thesis, comprehensive summary doctoralThesis text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| ردمك: | 978-91-7063-192-4 |
| العلاقة: | Karlstad University Studies, 1403-8099 ; 2008:33 |
| الإتاحة: | http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-1848Test |
| حقوق: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsndl.UPSALLA1.oai.DiVA.org.kau.1848 |
| قاعدة البيانات: | Networked Digital Library of Theses & Dissertations |
| ردمك: | 9789170631924 |
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