Search results for "method of characteristics"

Variational approach to the mechanics of metal V-belt systems

2005

The mechanical behaviour of metal V-belt drives is strongly dependent on the elastic properties of both the belt and the pulley, which influence the belt penetration into the groove and the sliding on the pulley wall. The distribution of tension and penetration is quite different from the rubber belts, which may be dealt with in the assumption of perfectly rigid pulleys. The restoring effect of the centrifugal forces of the plate elements has also to be taken into account. The present analysis considers the combination of all those effects, choosing a three parameter deformation function to describe the plate bending and applying the principle of virtual work for the calculation of the unkn…

Electroelastic Analysis of Piezoelectric Composite Laminates by Boundary Integral Equations

2004

A boundary integral representation for the electroelastic state in piezoelectric composite laminates subjected to axial extension, bending, torsion, shear/bending, and electric loadings is proposed. The governing equations are presented in terms of electromechanical generalized variables by the use of a suitable matrix notation. Thus, the three-dimensional electroelasticity solution for piezoelectric composite laminates is generated from a set of two partially coupled differential equations defined on the cross section of each individual ply within the laminate. These ply equations are linked through the interface conditions, which allow restoration of the model of the laminate as a whole. …

A numerical unsteady friction model for the transient flow arising during the filling process of intermittent water distribution systems.

2011

Multiscale Particle Method in Solving Partial Differential Equations

2007

A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.

Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme

2017

This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which leads to an efficient computation with a small number of degrees of freedom especially in three space dimensions. In this paper, Part II, we apply a semi-implicit time discretization which yields the linear scheme. We concentrate on the diffusive viscoelastic model, i.e. in the constitutive equation for time evolution of the conformation tensor a diffusive effect is included. Under mild stability condi…

Removability of a Level Set for Solutions of Quasilinear Equations

2005

In this paper, we study the removability of a level set for the solutions of quasilinear elliptic and parabolic equations of the second order. We show, under rather general assumptions on the coeff...

Walsh function analysis of 2-D generalized continuous systems

1990

The importance of the generalized or singular 2D continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables. A technique is presented for solving these systems in terms of Walsh functions. The method replaces the solution of a two-variable partial differential equation with the solution of a linear algebraic generalized 2D Sylvester equation. An efficient technique for the recursive solution of the latter equation is offered. All the results apply also in the usual Roesser 2D state-space case. >

Generalized Buckley–Leverett theory for two-phase flow in porous media

2011

Hysteresis and fluid entrapment pose unresolved problems for the theory of flow in porous media. A generalized macroscopic mixture theory for immiscible two-phase displacement in porous media (Hilfer 2006b Phys. Rev. E 73 016307) has introduced percolating and nonpercolating phases. It is studied here in an analytically tractable hyperbolic limit. In this limit a fractional flow formulation exists, that resembles the traditional theory. The Riemann problem is solved analytically in one dimension by the method of characteristics. Initial and boundary value problems exhibit shocks and rarefaction waves similar to the traditional Buckley-Leverett theory. However, contrary to the traditional th…

A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time

2004

The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

2016

The dispersionless Kadomtsev-Petviashvili (dKP) equation $(u_t+uu_x)_x=u_{yy}$ is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation $u_t+uu_x=0$. We show numerically that the solutions to the transformed equation do not develop shocks. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the $(x,y)$ plane, where the solution of the dKP equation exists in a weak sense only, and a…