Search results for "Euler"
showing 10 items of 159 documents
A two steps Lagrangian–Eulerian numerical model for the simulation of explosive welding of three dissimilar materials joints
2021
Abstract Explosion welding (EXW) is a solid-state joining process used to produce lap joints out of metal plates of dissimilar materials. During the process, a controlled explosive detonation results in a pressure wave pushing one of the plates to be welded, called flyer, against the other with high velocity. The high pressure and temperature generated, because of the impact energy decaying into heat, create the conditions for solid bonding phenomenon to take place. Due to the complexity of experimental tests, numerical simulation is considered a fundamental design tool for the process. Different approaches are found in literature to simulate the process. In this paper, a dual step Lagrangi…
The Application of CFD Methods for Modeling of a Three-Phase Fixed-Bed Reactor
2018
The mathematical model of the three-phase fixed-bed reactor (TBR) consisting of the continuity equation, the momentum balances of each phase and mass balances of reaction mixture components were presented and discussed. These balances are the result of averaging by means of Euler’s procedure and form the basis of the Computational Fluid Dynamics (CFD). Although the CFD model is based on fundamental principles some empirical relations (closure lows) must be implemented into the momentum balance in order to ensure a proper description of the dynamics of very complex three-phase system. Therefore, the sensitivity of a multiphase CFD model with respect to relations defining drag forces between …
DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
1998
Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010
Navier-Stokes equations on an exterior circular domain: construction of the solution and the zero viscosity limit
1997
Abstract In this Note, we consider the limit of Navier-Stokes equations on a circular domain. By an explicit construction of the solution, it is proved that, when viscosity goes to zero, solution converges to the Euler solution outside the boundary layer and to the Prandtl solution inside the boundary layer.
Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms
1999
SUMMARY A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensi…
Bicycle paths, elasticae and sub-Riemannian geometry
2020
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight lines, and that its infinite minimizing geodesics (or `metric lines') correspond to bike paths whose front tracks are either straight lines or `Euler's solitons' (also known as Syntractrix or Convicts' curves).
A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids
2019
A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained i…
Molecular shape analysis based upon the morse-smale complex and the connolly function
2003
Docking is the process by which two or several molecules form a complex. Docking involves the geometry of the molecular surfaces, as well as chemical and energetical considerations. In the mid-eighties, Connolly proposed a docking algorithm matching surface knobs with surface depressions. Knobs and depressions refer to the extrema of the Connolly function, which is defined as follows. Given a surface M bounding a three-dimensional domain X, and a sphere S centered at a point p of M, the Connolly function is equal to the solid angle of the portion of S containing within X.We recast the notions of knobs and depressions in the framework of Morse theory for functions defined over two-dimensiona…
A stabilized finite element method for particulate two-phase flow equations laminar isothermal flow
1997
A finite element method for the solution of particulate two-phase flows is presented. The governing system has the form of compressible Navier-Stokes equations with unknown pressure. Therefore, the proposed method must capture the main features of stabilized methods used for incompressible as well as for compressible Navier-Stokes equations. Solution of the resulting nonlinear algebraic system of equations is based on the linearization using Newton method in conjunction with Generalized Minimal Residual iterative solver and Incomplete LU preconditioning. The method has been tested for three test cases including venturi tube flow, flow over backward step and mixing of flows in t-junction.
On the moving load problem in Euler–Bernoulli uniform beams with viscoelastic supports and joints
2016
This paper concerns the vibration response under moving loads of Euler–Bernoulli uniform beams with translational supports and rotational joints, featuring Kelvin–Voigt viscoelastic behaviour. Using the theory of generalized functions to handle the discontinuities of the response variables at the support/joint locations, exact beam modes are obtained from a characteristic equation built as determinant of a (Formula presented.) matrix, for any number of supports/joints. Based on pertinent orthogonality conditions for the deflection modes, the response under moving loads is built in the time domain by modal superposition. Remarkably, all response variables are built in a closed analytical for…