Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, a numerical model based on a conserved-scalar approach is presented for buoyant ethanol-air wick diffusion flames at atmospheric and sub-mospheric conditions.
4 citations
TL;DR: In this paper, the velocity equations for axially symmetric flow of a perfectly plastic solid which obeys Tresca's yield condition and associated flow rule possess many symmetries.
Abstract: In kinematically determined regimes, the velocity equations for axially symmetric flow of a perfectly plastic solid which obeys Tresca's yield condition and associated flow rule possess many symmetries. These equations apply also to the flow of granular materials according to the ‘double-shearing’ theory of Spencer [1], [2]. Using Lie group methods, five classes of generalized self-similar solutions are identified. Special cases are the two types of solution due to Lippmann [3] [4] and the flow past a cone found by Spencer [5]. For each class of solution, determination of the stream function requires the solution of a second-order ordinary differential equation, which can in each case be reduced to the analysis of a first-order equation. Examples of the flow fields and corresponding streamlines for three of the four newly determined cases are computed numerically.
4 citations
01 Jan 1993
TL;DR: In this article, the numerical solution of a moving boundary hyperbolic problem with a shock front propagation in a constant state was considered. And the numerical convergence of the scheme was tested with respect to a particular example where an approximate similarity solution is known.
Abstract: We report some preliminary results related to the numerical solution of a moving boundary hyperbolic problem. The problem describes a shock front propagation in a constant state. For this problem an implicit first order difference scheme was considered. The numerical convergence of the scheme was tested with respect to a particular example where an approximate similarity solution is known. As a main result we found a way to assess the numerical accuracy even when the similarity solution does not exist.
4 citations
TL;DR: In this paper, a partially filled membrane container rests on an incline and the governing nonlinear equations are solved numerically, and similar similarity solutions that lead to universal shapes are found.
Abstract: A long partially filled membrane container rests on an incline. The governing nonlinear equations are solved numerically. Similarity solutions that lead to universal shapes are found. The relationships among inclination, volume, and tension are illustrated.
4 citations
TL;DR: In this paper, it was shown that the squeezing flow of an Oldroyd-B fluid from a tube with a prescribed time-dependent radius has an exact separable solution.
Abstract: It is shown that the squeezing flow of an Oldroyd-B fluid from a tube with a prescribed time-dependent radius has an exact separable solution. In the special case where the tube radius varies exponentially with time a similarity solution exists. However, in this case there is a critical Weissenberg number above which a component of the stress tensor increases without bound in time.
4 citations