# Similarity and Dimensional Methods in Mechanics

@inproceedings{Sedov1959SimilarityAD, title={Similarity and Dimensional Methods in Mechanics}, author={L. I. Sedov}, year={1959} }

Preface to Ninth Edition. Preface to Eighth Edition. Preface to Sixth Edition. Preface to Third Edition. Preface to First Edition. General Dimensional Theory for Different Quantities. Similarity, Modeling, and Various Examples of Application of the Dimensional Theory. Application to the Turbulence Theory and the Theory of a Viscous Fluid Motion. One-Dimensional Unsteady-State Gas Motions. Introduction to the Theory of Gas Machines. Application to Astrophysics Problems.

## 2,305 Citations

Similarity Analysis for Relativistic Flow in One Dimension

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Transformations and restrictions are applied to the equations of relativistic flow in one space dimension which reduce the problem to a consideration of simpler differential equations. The results…

Hidden Invariances in Problems of Two-Dimensional and Three-Dimensional Wall Jets for Newtonian and Non-Newtonian Fluids

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A generating functions approach elaborated by Vinogradov enables one to derive conservation laws for the above-mentioned problems and, as a consequence, to find new self-similarities of the Navier--Stokes equations.

Application of the pi-theorem to the similarity criteria of slow deformation of inhomogeneous viscous fluids

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Singularities: Formation, Structure, and Propagation

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Preface Part I. Setting the Scene: 1. What are singularities all about? 2. Blow-up 3. Similarity profile 4. Continuum equations 5. Local singular expansions 6. Asymptotic expansions of PDEs Part II.…

High-order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics

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Abstract In this paper we present an extension of our general high-order curvilinear finite element approach for solving the Euler equations in a Lagrangian frame [1] to the case of axisymmetric…

Properties of Solutions to Gas Dynamics Equations on a Rotating Plane: the Case of Motions with Uniform Deformation

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A system of ideal polytropic gas equations written in the Lagrangian coordinates is considered on a uniformly rotating plane. For this system the first integrals corresponding to motions with uniform…

Searching fundamental information in ordinary differential equations. Nondimensionalization technique

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A formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: they are physically interpreted as balances between counteracting quantities in the problem, and they are of the order of magnitude unity.

Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics

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- 1996

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena…

Analytic solutions for the three-dimensional compressible Navier?Stokes equation

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We investigate the three-dimensional compressible Navier–Stokes (NS) and the continuity equations in Cartesian coordinates for Newtonian fluids. The problem has an importance in different fields of…

Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases

- Mathematics, Physics
- 2012

We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically…