Optimum time-step size for 2D (2, 4) FDTD method

2011 ◽  
Vol 47 (5) ◽  
pp. 317 ◽  
Author(s):  
T.T. Zygiridis
Keyword(s):  
Fdtd Method ◽  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size

scholarly journals Investigation of Numerical Conditions of Moving Particle Semi-implicit for Two-Dimensional Wedge Slamming

2022 ◽  
Author(s):  
Takahito Iida ◽  
Yudai Yokoyama
Keyword(s):  
Particle Size ◽  
Poor Performance ◽  
Verification And Validation ◽  
Two Dimensional ◽  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size ◽  
Tuning Parameters ◽  
Moving Particle

AbstractThe sensitivity of moving particle semi-implicit (MPS) simulations to numerical parameters is investigated in this study. Although the verification and validation (V&V) are important to ensure accurate numerical results, the MPS has poor performance in convergences with a time step size. Therefore, users of the MPS need to tune numerical parameters to fit results into benchmarks. However, such tuning parameters are not always valid for other simulations. We propose a practical numerical condition for the MPS simulation of a two-dimensional wedge slamming problem (i.e., an MPS-slamming condition). The MPS-slamming condition is represented by an MPS-slamming number, which provides the optimum time step size once the MPS-slamming number, slamming velocity, deadrise angle of the wedge, and particle size are decided. The simulation study shows that the MPS results can be characterized by the proposed MPS-slamming condition, and the use of the same MPS-slamming number provides a similar flow.

scholarly journals Precise-Integration Time-Domain Formulation for Optical Periodic Media

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7896
Author(s):  
Joan Josep Sirvent-Verdú ◽  
Jorge Francés ◽  
Andrés Márquez ◽  
Cristian Neipp ◽  
Mariela Álvarez ◽  
...  
Keyword(s):  
Time Domain ◽  
Fdtd Method ◽  
Fdtd Simulation ◽  
Integration Time ◽  
Periodic Media ◽  
Step Size ◽  
Time Step ◽  
Precise Integration ◽  
Time Step Size ◽  
Wide Range

A numerical formulation based on the precise-integration time-domain (PITD) method for simulating periodic media is extended for overcoming the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the periodic boundary conditions are implemented, permitting the simulation of a wide range of periodic optical media, i.e., gratings, or thin-film filters. Furthermore, the complete tensorial derivation for the permittivity also allows simulating anisotropic periodic media. Numerical results demonstrate that PITD is reliable and even considering anisotropic media can be competitive compared to traditional FDTD solutions. Furthermore, the maximum allowable time-step size has been demonstrated to be much larger than that of the CFL limit of the FDTD method, being a valuable tool in cases in which the steady-state requires a large number of time-steps.

A discussion about optimum time step size and maximum simulation time in EMTP-based programs

2015 ◽  
Vol 72 ◽  
pp. 24-32 ◽  
Author(s):  
José Carlos G. de Siqueira ◽  
Benedito D. Bonatto ◽  
José R. Martí ◽  
Jorge A. Hollman ◽  
Hermann W. Dommel
Keyword(s):  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size ◽  
Simulation Time

scholarly journals The Effect of Iterative Procedures on the Robustness and Fidelity of Augmented Lagrangian SPH

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 472
Author(s):  
Deniz Can Kolukisa ◽  
Murat Ozbulut ◽  
Mehmet Yildiz
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Augmented Lagrangian ◽  
Reynolds Numbers ◽  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Spatial Derivatives

The Augmented Lagrangian Smoothed Particle Hydrodynamics (ALSPH) method is a novel incompressible Smoothed Particle Hydrodynamics (SPH) approach that solves Navier–Stokes equations by an iterative augmented Lagrangian scheme through enforcing the divergence-free coupling of velocity and pressure fields. This study aims to systematically investigate the time step size and the number of inner iteration parameters to boost the performance of the ALSPH method. Additionally, the effect of computing spatial derivatives with two alternative schemes on the accuracy of numerical results are also scrutinized. Namely, the first scheme computes spatial derivatives on the updated particle positions at each iteration, whereas the second one employs the updated pressure and velocity fields on the initial particle positions to compute the gradients and divergences throughout the iterations. These two schemes are implemented to the solution of a flow over a circular cylinder at Reynolds numbers of 200 in two dimensions. Initially, simulations are performed in order to determine the optimum time step sizes by utilizing a maximum number of five iterations per time step. Subsequently, the optimum number of inner iterations is investigated by employing the predetermined optimum time step size under the same flow conditions. Finally, the schemes are tested on the same flow problem with different Reynolds numbers using the best performing combination of the aforementioned parameters. It is observed that the ALSPH method can enable one to increase the time step size without deteriorating the numerical accuracy as a consequence of imposing larger ALSPH penalty terms in larger time step sizes, which, overall, leads to improved computational efficiency. When considering the hydrodynamic flow characteristics, it can be stated that two spatial derivative schemes perform very similarly. However, the results indicate that the derivative operation with the updated particle positions produces slightly lower velocity divergence magnitudes at larger time step sizes.

scholarly journals An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1575 ◽  
Author(s):  
Zhen Kang ◽  
Ming Huang ◽  
Weilin Li ◽  
Yufeng Wang ◽  
Fang Yang
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Fdtd Method ◽  
Magnetized Plasma ◽  
Numerical Dispersion ◽  
Step Size ◽  
Time Step ◽  
Precise Integration ◽  
Dispersion Error ◽  
Time Step Size

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

Optimum time step size and maximum simulation time in EMTP-based programs

2014 ◽  
Author(s):  
Jose Carlos G. de Siqueira ◽  
Benedito D. Bonatto ◽  
Jose R. Marti ◽  
Jorge A. Hollman ◽  
Hermann W. Dommel
Keyword(s):  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size ◽  
Simulation Time

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

Sign in / Sign up

Export Citation Format

Share Document