Solution of the Boltzmann equation at the singular points in a shock wave by the method of rational truncation and coordinate straining

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dc.contributor.authorMcGregor, Roy Danielen_US
dc.date.accessioned2024-08-14T22:46:15Z
dc.date.available2024-08-14T22:46:15Z
dc.date.copyright1976en_US
dc.date.issued1976
dc.degree.departmentDepartment of Physics
dc.degree.departmentDepartment of Physics and Astronomy
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractA solution of the Boltzmann equation at the upstream and down­stream singular points in a shock wave, for the case of Maxwell molecules, is obtained by application of the method of rational trun­cation and coordinate straining. The method is based of the idea that a rational procedure for truncating and closing any system of moment equations must be developed from an orthonormal expansion for the distribution function, and that the convergence of the expansion can be accelerated if the coordinates in velocity space are scaled in accordance with the nature of the distribution function. The use of an orthonormal expansion for the distribution function is shown to yield significant improvement over the method of Grad, but the further step of coordinate straining is necessary to provide a rapidly convergent solution. The solution shows that the Navier-Stokes and Fourier relations (ie., first-order Chapman-Enskog results) are approximately valid only for weak shock waves; confirms the existence of temperature overshoot in strong shock waves; and provides exact boundary values that can be used to guide numerical solutions of the Boltzmann equation for shock-wave structure.en_US
dc.format.extent49 pages
dc.identifier.urihttps://hdl.handle.net/1828/18927
dc.rightsAvailable to the World Wide Weben_US
dc.titleSolution of the Boltzmann equation at the singular points in a shock wave by the method of rational truncation and coordinate strainingen_US
dc.typeThesisen_US

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