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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20 Jan 1969
TL;DR: In this article, a simple interaction analysis based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave was proposed to calculate the major features of the interaction between a laminar boundary layer and a supersonic corner expansion wave.
Abstract: There are three distinct effects involved in the interaction of a laminar boundary layer and a supersonic corner expansion wave. These are: the upstream influence effect causing some pressure decay ahead of the corner, transverse pressure gradients in the immediate neighborhood of the corner, and the interaction of the boundary layer downstream with the external flow. Arguments are presented to suggest that, when the flow is locally hypersonic and the wall is highly cooled, the dominant effect is the downstream interaction process. Hence the major features can be calculated by using a simple interaction analysis down stream of the corner based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave. Numerical results are obtained by using the "cold wall" similarity solution to the boundary-layer equations. These show that pressure decay extends over a region which can be many times larger than the original plate length used to generate the boundary layer.
TL;DR: In this paper, a numerical method for scalar conservation laws in one space dimension is presented, where the solution is represented by particles that carry function values and move according to the method of characteristics, and an interpolation is defined by an analytical similarity solution of the conservation law.
Abstract: We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.
TL;DR: In this paper, an unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained.
Abstract: Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time t and position x, the rivulet widens or narrows according to (x − ct), where c is velocity of a rivulet, and the film thickens or thins according to a free parameter F0, independent of power-law index N. The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.
01 Jan 2014
TL;DR: The 15th International Conference of International Academy of Physical Sciences Dec 9 - 13, 2012, Pathumthani, Thailand as mentioned in this paper was the first one to recognize the work of the authors of this paper.
Abstract: The 15th International Conference of International Academy of Physical Sciences Dec 9 - 13, 2012, Pathumthani, Thailand.
05 Mar 2023-Proceedings Of The Institution Of Mechanical Engineers, Part E: Journal Of Process Mechanical Engineering
TL;DR: In this article , the authors applied the Keller box method to the one-phase moving boundary problem with moving phase change material, size-dependent thermal conductivity, and periodic boundary conditions.
Abstract: The Keller box method is applied to the one-phase moving boundary problem with moving phase change material, size-dependent thermal conductivity, and periodic boundary conditions. The phase transition process is allowed to occur when the material is forced to move in one direction or the other at a constant speed. The boundary immobilization method is applied to immobilize the moving boundary, and for the numerical approximation of moving boundary problem, we proposed Keller box method. Keller box method also accommodates the non-linearity in thermal conductivity and Stefan condition. Using the convergence analysis, the proposed scheme obtains stability, as well as second-order accuracy for both spatial and temporal directions, under reasonable conditions. To validate the proposed numerical scheme, we have considered a particular case of this problem having a similarity solution. It is found that the numerical results obtained by the Keller box method have good agreement with the similarity solution and also verified that the computational rate of convergence of our scheme is two. The effects of various parameters and size-dependent thermal conductivity on the position of moving boundary are also investigated.