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Showing 1 to 9 of 9 for “"Similarity solutions"”.
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Similarity solutions of stochastic nonlinear parabolic equations
… introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is …
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Similarity Solutions for the Two-Dimensional Diffusion–Advection Equation in Sharp-Corner Geometries
… the 2D diffusion-advection equation to obtain a similarity ansatz, reducing the equation to a time-independent second-order PDE. By modifying the ansatz, the problem can be recast as an eigenvalue problem. Exploiting elliptic regularity and the strong maximum principle, we invoke the Krein-Rutman …
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A finite difference solution to the two-dimensional wall jet on a combustion turbine blade
… cases are compared with the Falkner-Skan similarity solutions. Results from the finite difference calculation for the turbulent, noninj ected cases are compared with a two-parameter integral analysis. The boundary-layer calculation is applied to wall-jet injection near the leading edge of …
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Applications of Lie Groups in Turbulence Modeling
… problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for …
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Self similar flows in finite or infinite two dimensional geometries
… flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It …
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Laminar fluid flow, particle transport and permeate flux behavior in crossflow membrane filters
Similarity solutions for axial and lateral velocity profiles, pressure gradients and wall skin friction are derived for the laminar, isothermal single phase flow of incompressible fluids in channels having porous boundaries. Results from a finite difference solution to the vorticity-stream function …
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Spreading of viscous fluids and granular materials on slopes
… surfaces with different shapes are described by similarity solutions to address problems motivated by engineering as well as geophysical applications. Pouring viscous fluid out of a container can be a frustratingly slow process depending on the shape and the degree of tipping of the container. …
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The evolution of ocean fronts in the presence of mixed layer turbulence
… forcing this advection-diffusion equation admits similarity solutions describing a spreading front where the spreading results from shear dispersion associated with the cross-front flow and vertical diffusion of density. In response to shear dispersion, the front evolves towards a density profile …
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The Influence of Layering and Time-Dependent Injection Rates on Gravity-Driven Flows in Porous Media
… in each layer have on the flow, finding similarity solutions which we validate with numerics and experiments. In chapter 4 we extend this model to consider not only a change in permeability but also a change in the elevation of the cap rock at the interface between two regions. We …