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THEORETICAL AND APPLIED MECHANICS |
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TEORIJSKA I PRIMENJENA MEHANIKA 2005 Vol.32 (1), pp.39-64 |
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Summary: |
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A variational approach to the shock structure problem
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A variational approach to the shock structure problem is proposed. The set
of governing equations, consisted of n first-order
ordinary differential equations accompanied with 2n boundary
conditions at ±¥,
is put into variational form by means of least-squares method. The
corresponding variational principle is adjusted for application of Ritz
method. This direct method is used for construction of approximate
analytical solutions to the shock structure problem and derivation of the
estimates for the shock thickness. General procedure is applied to the
study of Burgers' equation and equations of gas dynamics. |
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