scholarly journals A Fast Poisson Solver of Second-order Accuracy for Isolated Systems in Three-dimensional Cartesian and Cylindrical Coordinates

2019 ◽  
Vol 241 (2) ◽  
pp. 24 ◽  
Author(s):  
Sanghyuk Moon ◽  
Woong-Tae Kim ◽  
Eve C. Ostriker
Keyword(s):  
Three Dimensional ◽  
Second Order ◽  
Cylindrical Coordinates ◽  
Order Accuracy ◽  
Poisson Solver ◽  
Fast Poisson Solver ◽  
Isolated Systems

scholarly journals High Order Godunov Type Multimesh Method for 3d Impact Problems of Elastoplastic Media

2021 ◽  
Keyword(s):  
Three Dimensional ◽  
Second Order ◽  
The Body ◽  
Godunov Scheme ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Sharp Interface Method ◽  
Impact Problems ◽  
Elastoplastic Media ◽  
Compact Stencil

A numerical method for calculating the three-dimensional processes of impact interaction of elastoplastic bodies under large displacements and deformations based on the multi mesh sharp interface method and modified Godunov scheme is presented. To integrate the equations of dynamics of an elastoplastic medium, the principle of splitting in space and in physical processes is used. The solutions of the Riemann problem for first and second order accuracy for compact stencil for an elastic medium in the case of an arbitrary stress state are obtained and presented, which are used at the “predictor” step of the Godunov scheme. A modification of the scheme is described that allows one to obtain solutions in smoothness domains with a second order of accuracy on a compact stencil for moving Eulerian-Lagrangian grids. Modification is performed by converging the areas of influence of the differential and difference problems for the Riemann’s solver. The “corrector” step remains unchanged for both the first and second order accuracy schemes. Three types of difference grids are used. The first – a moving surface grid – consists of a continuous set of triangles that limit and accompany the movement of bodies; the size and number of triangles in the process of deformation and movement of the body can change. The second – a regular fixed Eulerian grid – is limited to a surface grid; separately built for each body; integration of equations takes place on this grid; the number of cells in this grid can change as the body moves. The third grid is a set of local Eulerian-Lagrangian grids attached to each moving triangle of the surface from the side of the bodies and allowing obtain the parameters on the boundary and contact surfaces. The values of the underdetermined parameters in cell’s centers near the contact boundaries on all types of grids are interpolated. Comparison of the obtained solutions with the known solutions by the Eulerian-Lagrangian and Lagrangian methods, as well as with experimental data, shows the efficiency and sufficient accuracy of the presented three-dimensional methodology.

Construction of Space-Time High Resolution Second Order Accurate Three Dimensional MP Difference Schemes

2006 ◽  
Vol 306-308 ◽  
pp. 685-690
Author(s):  
Kai-Teng Wu ◽  
Jian Guo Ning
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Natural Extension ◽  
Three Dimensional ◽  
Second Order ◽  
Difference Schemes ◽  
Vector System ◽  
Maximum Principles ◽  
General Context ◽  
Three Dimension ◽  
Order Accuracy

In this paper, a new Riemann-solver-free class of difference schemes are constructed to scalar nonlinear hyperbolic conservation laws in the three dimension (3D). We proved that these schemes had second order accuracy in space and time, and satisfied maximum principles (marked as MPs) under an appropriate CFL condition. This results in a second-order accuracy, MP schemes a natural extension of the one (two)-dimensional second-order. In addition, these schemes can still be extended to the vector system of conservation law. We yet prove that these schemes satisfied the scalar and vector maximum principle, and in the more general context of systems.

AN ACOUSTIC FINITE-DIFFERENCE TIME-DOMAIN ALGORITHM WITH ISOTROPIC DISPERSION

2005 ◽  
Vol 13 (02) ◽  
pp. 365-384 ◽  
Author(s):  
CHRISTOPHER L. WAGNER ◽  
JOHN B. SCHNEIDER
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Phase Error ◽  
Three Dimensional ◽  
Second Order ◽  
Step Size ◽  
Order Accuracy ◽  
Discretization Step ◽  
Difference Time

The classic Yee Finite-Difference Time-Domain (FDTD) algorithm employs central differences to achieve second-order accuracy, i.e., if the spatial and temporal step sizes are reduced by a factor of n, the phase error associated with propagation through the grid will be reduced by a factor of n2. The Yee algorithm is also second-order isotropic meaning the error as a function of the direction of propagation has a leading term which depends on the square of the discretization step sizes. An FDTD algorithm is presented here that has second-order accuracy but fourth-order isotropy. This algorithm permits a temporal step size 50% larger than that of the three-dimensional Yee algorithm. Pressure-release resonators are used to demonstrate the behavior of the algorithm and to compare it with the Yee algorithm. It is demonstrated how the increased isotropy enables post-processing of the simulation spectra to correct much of the dispersion error. The algorithm can also be optimized at a specified frequency, substantially reducing numerical errors at that design frequency. Also considered are simulations of scattering from penetrable spheres ensonified by a pulsed plane wave. Each simulation yields results at multiple frequencies which are compared to the exact solution. In general excellent agreement is obtained.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

A Domain-Decomposed Fast Poisson Solver on a Rectangle

1987 ◽  
Vol 8 (1) ◽  
pp. s14-s26 ◽  
Author(s):  
Tony F. Chan ◽  
Diana C. Resasco
Keyword(s):  
Poisson Solver ◽  
Fast Poisson Solver

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

2021 ◽  
Vol 10 (9) ◽  
pp. 3273-3282
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Flow Model ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

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