Fully Coupled Time Domain Modelling of 3D Floating Bodies and Mooring Systems in Regular and Irregular Sea States

2012 ◽  
Author(s):  
Kameswara S. Vepa ◽  
Diederik Van Nuffel ◽  
Wim Van Paepegem ◽  
Joris Degrieck
Keyword(s):  
Time Domain ◽  
Domain Size ◽  
Floating Body ◽  
Computational Time ◽  
Floating Bodies ◽  
Step Size ◽  
Coupled Models ◽  
Time Step ◽  
Time Step Size ◽  
Fully Coupled

Research on floating bodies like Wave Energy Converters (WECs) and Laser Imaging Detection And Ranging (LIDAR) systems has recently known a large growth. To study the minute details of the working model, it is important to study the effect of interactions between the waves, floating bodies and the mooring systems that are controlling the motion of the floating body. To achieve a more realistic numerical model in the time domain, a number of programs are linked together. The idea is to use the strength of each individual program for better results and also reduce the computational time. This paper provides a solution in the direction of using a fully coupled time domain coupling code that controls the data flow between a fluid solver, a structural solver, and a kinematic system simulator. Two- and three-dimensional fully coupled models are studied for calculation times and accuracy of results, and scaling is tested through parallelization on a large HPC cluster. The time step size of the whole model can be controlled by the user. Calculation times and memory requirements vary largely based on the factors like: domain size, SPH particle size, material model used for the floating body and the mooring system, complexity of the mechanical system inside the floating body. As a test case, a rigid body model is presented in this paper.

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.

Thorough Verification and Validation of CFD Prediction of FPSO Current Load for Confident Applications

2019 ◽  
Author(s):  
Wei Xu ◽  
Zhenjia (Jerry) Huang ◽  
Hyunjoe Kim
Keyword(s):  
Mesh Refinement ◽  
Domain Size ◽  
Development Project ◽  
Transverse Load ◽  
Cfd Modeling ◽  
Current Load ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Rans Model

Abstract In this paper, a thorough verification of FPSO current load modeling and simulation using CFD was carried out and a modeling practice developed in a joint development project [1] was adopted. The towing test data obtained with thorough quality assurance process were used as benchmark data in the verification work. To have high confidence in the CFD modeling and simulations, both steady simulations with RANS model and unsteady simulations with IDDES model were carried out. For the steady simulations, sensitivity checks were carried out for the domain size, mesh refinement, turbulence models, boundary conditions and Reynolds effect. For unsteady simulations, the wake zone mesh refinement, time step size, number of inner iterations and different RANS model for boundary layers were considered during the sensitivity verification stage. It was found in this study that the transverse load (Fy) and yaw moment (Mz) of the FPSO can be predicted fairly well using RANS model, while the DES model needs to be adopted in order to accurately predict the longitudinal forces (Fx) at certain range of current directions. The wake grid for the DES needs to be fine enough in order to capture the details of vortices and the running time trace needs to be long enough to reduce the sensitivity on the mean current forces.

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.

The impact of the inverse chirp z-transform on breast microwave radar image reconstruction

2020 ◽  
Vol 12 (9) ◽  
pp. 848-854
Author(s):  
Tyson Reimer ◽  
Mario Solis-Nepote ◽  
Stephen Pistorius
Keyword(s):  
Image Reconstruction ◽  
Time Domain ◽  
Tumor Response ◽  
Imaging System ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Inverse Discrete Fourier Transform ◽  
Microwave Radar ◽  
The Impact

This work examines the impact of the inverse chirp z-transform (ICZT) for frequency-to-time-domain conversion during image reconstruction of a pre-clinical radar-based breast microwave imaging system operating over 1–8 GHz. Two anthropomorphic breast phantoms were scanned with this system, and the delay-multiply-and-sum beamformer was used to reconstruct images of the phantoms, after using either the ICZT or the inverse discrete Fourier transform (IDFT) for frequency-to-time domain conversion. The contrast, localization error, and presence of artifacts in the reconstructions were compared. The use of the IDFT resulted in prominent ring artifacts that were not present when using the ICZT, and the use of the ICZT resulted in higher contrast between the tumor and clutter responses. In one of the phantoms, the tumor response was only visible in reconstructions that used the ICZT. The use of the ICZT evaluated with a time-step size of 11 ps resulted in the reduction of prominent artifacts present when using the IDFT and the successful identification of the tumor response in the reconstructed images.

Columnar to Equiaxed Transition During Ingot Casting Using Ternary Alloy Composition

2010 ◽  
Vol 649 ◽  
pp. 349-354 ◽  
Author(s):  
Laszlo Könözsy ◽  
Anton Ishmurzin ◽  
Monika Grasser ◽  
Meng Huai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Ternary Alloy ◽  
Alloy Composition ◽  
Species Conservation ◽  
Computational Time ◽  
Columnar Dendrite ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Columnar To Equiaxed Transition ◽  
The Right

The present paper deals with the formation of macrosegregation in a benchmark ingot using (Fe-C-Cr) ternary alloy composition. The numerical investigation of complex multiphase phenomena is a difficult study, because the thermophysical properties depend strongly on the temperature, concentration, pressure and chemical composition as well. For the numerical modeling of solidification and melting processes different phases (e.g. liquid, equiaxed crystals and columnar dendrite trunks) have been considered. The mass, momentum, energy conservation and species conservation equations for each phase have been solved. The Eulerian-Eulerian model equations have been implemented in the commercial Finite Volume Method based FLUENT-ANSYS v6.3 CFD software using User-Defined Functions (UDF). The mass transfer has been modelled by diffusion controlled crystal growth by applying an advanced tip tracking algorithm for columnar solidification. The modeling of the grain density transport has been improved. The derivatives of the mass fraction quantities for each component appear in the nucleation rate term. It means that we obtain a new term of the right hand side of the grain density transport equation for using ternary alloy composition. This paper focuses on both the process and simulation parameters and their influence on the macrosegregation formation. The results show that the macrosegregation pattern does not change significantly above a well-chosen number of grid cells, and the computational time could be decreased, when the time step size has been increased.

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.

On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

2021 ◽  
Author(s):  
Ethan Corle ◽  
Matthew Floros ◽  
Sven Schmitz
Keyword(s):  
Experimental Data ◽  
Particle Method ◽  
Comprehensive Analysis ◽  
Solution Stability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Vortex Particle Method ◽  
Whirl Flutter ◽  
Vortex Particle

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

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