Test Problems Based on Lamé Superspheres

2007 ◽  
pp. 922-936 ◽  
Author(s):  
Michael T. M. Emmerich ◽  
André H. Deutz
Keyword(s):  
Test Problems

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

scholarly journals Approximate Solutions of Time Fractional Diffusion Wave Models

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 923 ◽  
Author(s):  
Abdul Ghafoor ◽  
Sirajul Haq ◽  
Manzoor Hussain ◽  
Poom Kumam ◽  
Muhammad Asif Jan
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Quadrature Rule ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Haar Wavelets ◽  
Test Problems ◽  
Algebraic Equations ◽  
Diffusion Wave ◽  
Wave Models

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

scholarly journals A finite volume method for two-moment cosmic-ray hydrodynamics on a moving mesh

2021 ◽  
Author(s):  
T Thomas ◽  
C Pfrommer ◽  
R Pakmor
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Source Term ◽  
Cosmic Ray ◽  
Moving Mesh ◽  
Test Problems ◽  
Integration Step ◽  
Custom Made ◽  
Anisotropic Transport ◽  
Volume Method

Abstract We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfvén waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

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