Computationally efficient modeling of hydro-sediment-morphodynamic processes using a hybrid local time step/global maximum time step

2019 ◽  
Vol 127 ◽  
pp. 26-38 ◽  
Author(s):  
Peng Hu ◽  
Yunlong Lei ◽  
Jianjian Han ◽  
Zhixian Cao ◽  
Huaihan Liu ◽  
...  
Keyword(s):  
Local Time ◽  
Global Maximum ◽  
Computationally Efficient ◽  
Time Step ◽  
Maximum Time ◽  
Efficient Modeling

scholarly journals A Computationally Efficient Shallow Water Model for Mixed Cohesive and Non-Cohesive Sediment Transport in the Yangtze Estuary

Water ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1435
Author(s):  
Peng Hu ◽  
Junyu Tao ◽  
Aofei Ji ◽  
Wei Li ◽  
Zhiguo He
Keyword(s):  
Sediment Transport ◽  
Yangtze Estuary ◽  
Water Model ◽  
Cohesive Sediments ◽  
Shallow Water Model ◽  
Computationally Efficient ◽  
Time Step ◽  
The Yangtze Estuary ◽  
Erosion Coefficient ◽  
Cohesive Sediment Transport

In this paper, a computationally efficient shallow water model is developed for sediment transport in the Yangtze estuary by considering mixed cohesive and non-cohesive sediment transport. It is firstly shown that the model is capable of reproducing tidal-hydrodynamics in the estuarine region. Secondly, it is demonstrated that the observed temporal variation of suspended sediment concentration (SSC) for mixed cohesive and non-cohesive sediments can be well-captured by the model with calibrated parameters (i.e., critical shear stresses for erosion/deposition, erosion coefficient). Numerical comparative studies indicate that: (1) consideration of multiple sediment fraction (both cohesive and non-cohesive sediments) is important for accurate modeling of SSC in the Yangtze Estuary; (2) the critical shear stress and the erosion coefficient is shown to be site-dependent, for which intensive calibration may be required; and (3) the Deepwater Navigation Channel (DNC) project may lead to enhanced current velocity and thus reduced sediment deposition in the North Passage of the Yangtze Estuary. Finally, the implementation of the hybrid local time step/global maximum time step (LTS/GMaTS) (using LTS to update the hydro-sediment module but using GMaTS to update the morphodynamic module) can lead to a reduction of as high as 90% in the computational cost for the Yangtze Estuary. This advantage, along with its well-demonstrated quantitative accuracy, indicates that the present model should find wide applications in estuarine regions.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

scholarly journals Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

2012 ◽  
Vol 78 (4) ◽  
pp. 469-482 ◽  
Author(s):  
B. M. COWAN ◽  
S. Y. KALMYKOV ◽  
A. BECK ◽  
X. DAVOINE ◽  
K. BUNKERS ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Cylindrical Symmetry ◽  
Small Time ◽  
Numerical Dispersion ◽  
Computationally Efficient ◽  
Plasma Bubble ◽  
Time Step ◽  
Simulation Code ◽  
Particle In Cell ◽  
Comput Phys

AbstractElectron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code vorpal (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys.196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code calder-circ (Lifschitz, A. F. et al. 2009 Particle-in-cell modelling of laser-plasma interaction using Fourier decomposition. J. Comput. Phys.228(5), 1803–1814) uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of two simulations indicates that these are free of numerical artefacts. Both approaches thus retrieve the physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver.

scholarly journals Accelerated Runge-Kutta Methods

2008 ◽  
Vol 2008 ◽  
pp. 1-38 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Artin Farahani
Keyword(s):  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Integration Schemes ◽  
Local Accuracy ◽  
Numerical Integrators ◽  
One Step ◽  
Runge Kutta ◽  
Finite Step ◽  
Proof Of Convergence

Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that are two-step in nature. For orders 3, 4, and 5, they require only 2, 3, and 5 function evaluations per time step, respectively. Therefore, they are more computationally efficient at achieving the same order of local accuracy. We present here the derivation and optimization of these accelerated integration methods. We include the proof of convergence and stability under certain conditions as well as stability regions for finite step sizes. Several numerical examples are provided to illustrate the accuracy, stability, and efficiency of the proposed methods in comparison with standard Runge-Kutta methods.

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