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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, the two-dimensional turbulent buoyant jet is analyzed using a vertical length scale defined by L = M0F0-F0−23 where Ma is the rate at which momentum is added at the source and F0 is the ratio x/L directly controls the bouyancy term.
Abstract: The two-dimensional turbulent buoyant jet is analyzed using a vertical length scale defined by L = M0F0 F0−23 where Ma is the rate at which momentum is added at the source and F0 is the rate at which buoyancy is added. Introduction of the length scales into the equations of motion shows the ratio x/L directly controls the bouyancy term. The pure momentum jet corresponds to the limit x/L→;0 and the pure buoyant plume to x/L→∞. Utilizing an eddy viscosity model, a similarity solution is presented for the buoyant plume, a series solution is used to develop this eddy viscosity model, and a numerical solution is presented for the buoyant jet. Comparisons are made with available experimental data.
2 citations
TL;DR: In this paper, the authors present a general mathematical static analysis of a fully liquid-filled geosynthetic-tube membrane section anchored on an incline, which can be modeled analytically as a set of simultaneous nonlinear ordinary differential equations with some undetermined boundary conditions.
Abstract: Membranes, such as geosynthetic tubes, have been widely used in civil construction and as storage tanks. Estimation of the shape, structural tension, and internal pressure are essential for effective and safe use of these structures. Motivated by a numerical study on the case of a partially liquid-filled membrane, this study presents a novel general mathematical static analysis of a fully liquid-filled geosynthetic-tube membrane section anchored on an incline. The membrane problem can be modeled analytically as a set of simultaneous nonlinear ordinary differential equations with some undetermined boundary conditions. A close examination of possible analytical solutions for increasing the cross-sectional area of the membrane identifies that the membrane sections have four similarity (or canonical) shapes. Integration of the curvature expression results in a similarity solution of the canonical shape, expressed in terms of analytical elliptic integrals. Using the analysis method developed, the range...
2 citations
12 Sep 2019
TL;DR: In this article, the authors derived a new system of ordinary differential equations, which depends on a single similarity variable and the boundary conditions are obtained from the Rankine-Hugoniot conditions for a strong shock.
Abstract: The spherical shock wave in a rarefied polyatomic gas is analyzed based on Rational Extended Thermodynamics (RET) with six independent fields; the mass density, velocity, pressure and dynamic pressure. By adopting the method on the basis of Lie group theory proposed in [A. Donato and T. Ruggeri, Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas, Journal of Mathematical Analysis and Applications, 251, (2000) 395-405], we derive a new system of ordinary differential equations, which depends on a single similarity variable. The boundary conditions are obtained from the Rankine- Hugoniot conditions for a strong shock. It is shown that the similarity solution is characterized by only one parameter and the preliminary numerical results address the important role of the dynamic pressure on the profile, which is different from the one of the well-known Sedov-von Neumann-Taylor solution.The spherical shock wave in a rarefied polyatomic gas is analyzed based on Rational Extended Thermodynamics (RET) with six independent fields; the mass density, velocity, pressure and dynamic pressure. By adopting the method on the basis of Lie group theory proposed in [A. Donato and T. Ruggeri, Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas, Journal of Mathematical Analysis and Applications, 251, (2000) 395-405], we derive a new system of ordinary differential equations, which depends on a single similarity variable. The boundary conditions are obtained from the Rankine- Hugoniot conditions for a strong shock. It is shown that the similarity solution is characterized by only one parameter and the preliminary numerical results address the important role of the dynamic pressure on the profile, which is different from the one of the well-known Sedov-von Neumann-Taylor solution.
2 citations
TL;DR: One-parameter continuous groups of transformations are applied to reduce a system of conservation laws with discontinuous initial conditions to a nonlinear ordinary differential equation with corresponding initial conditions and the associated Rankine-Hugoniot relations.
2 citations
TL;DR: In this article, a matched asymptotic solution for the flow of a Newtonian fluid under no-slip boundary conditions was proposed, and the predicted velocity and pressure profiles agree nearly quantitatively with CFD simulated values.
2 citations