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.

A highly stable explicit scheme for a fourth-order nonlinear diffusion filter

2020 ◽  
Vol 11 (04) ◽  
pp. 2050030
Author(s):  
Mahipal Jetta
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Fourth Order ◽  
Nonlinear Diffusion ◽  
Splitting Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Diffusion Filter ◽  
Spatial Derivatives

The standard finite difference scheme (forward difference approximation for time derivative and central difference approximations for spatial derivatives) for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results. The alternating directional implicit (ADI) splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size. In this paper, we develop [Formula: see text] stencils for the approximation of second-order spatial derivatives based on the finite pointset method. We then make use of these stencils for approximating the fourth-order partial differential equation. We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme, without compromising on the quality of the filtered image. Further, we demonstrate through numerical simulations that the proposed scheme is more efficient, in obtaining quality filtered image, than an ADI splitting scheme.

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.

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

Purely Meshless Smoothed Particle Hydrodynamics Computations of Taylor Vortex Flows

2007 ◽  
Author(s):  
Josep Salvans-Tort ◽  
Haris J. Catrakis
Keyword(s):  
Turbulent Flows ◽  
Smoothed Particle Hydrodynamics ◽  
Stokes Equations ◽  
Void Formation ◽  
Taylor Vortex ◽  
Vortex Flows ◽  
Time Step ◽  
Particle Spacing ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A purely meshless implementation of SPH (Smoothed Particle Hydrodynamics) is investigated to validate the accuracy of SPH as a method for fully meshless computations of Taylor vortex flows, i.e. without the need for any particle re-meshing. The continuity and Navier-Stokes equations together with appropriate initial and boundary conditions, as well as an equation of state, are solved for water using purely meshless SPH, i.e. in which no re-meshing of smoothed particles is employed. The exact analytical unsteady solution is compared with the SPH computational results and good agreement is found. The results show that it is not necessary to employ particle re-meshing, which had previously been claimed to be an essential ingredient for SPH simulations of Taylor vortex flows. In the present purely meshless SPH simulations, regular as well as irregular initial distributions of smoothed particles are investigated with the minimum inter-particle spacing scale and maximum interparticle void scale monitored as functions of time to ensure limited particle clustering, spreading, and void formation. Our results show convergence of the computed solution to the analytical solution, with increasing number of the smoothed particles and with decreasing time step. In our computations, the highest-order derivatives corresponding to the viscous terms are directly computed, i.e. without any artificial viscosity. These findings suggest the utility of this approach as a promising tool for purely meshless SPH direct numerical simulations and large-eddy simulations of turbulent flows.

The Comparison of Viscous Force Approximations of Smoothed Particle Hydrodynamics in Poiseuille Flow Simulation

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Zhengang Liu ◽  
Zhenxia Liu
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Flow Simulation ◽  
Reynolds Numbers ◽  
Viscous Force ◽  
Numerical Instability ◽  
Viscous Stress ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Particle Approximation ◽  
Poiseuille Flows

Poiseuille flows at two Reynolds numbers (Re) 2.5 × 10−2 and 5.0 are simulated by two different smoothed particle hydrodynamics (SPH) schemes on regular and irregular initial particles' distributions. In the first scheme, the viscous stress is calculated directly by the basic SPH particle approximation, while in the second scheme, the viscous stress is calculated by the combination of SPH particle approximation and finite difference method (FDM). The main aims of this paper are (a) investigating the influences of two different schemes on simulations and reducing the numerical instability in simulating Poiseuille flows discovered by other researchers and (b) investigating whether the similar instability exists in other cases and comparing results with the two viscous stress approximations. For Re = 2.5 × 10−2, the simulation with the first scheme becomes instable after the flow approaches to steady-state. However, this instability could be reduced by the second scheme. For Re = 5.0, no instability for two schemes is found.

Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Alexander Epple ◽  
Carlo L. Bottasso
Keyword(s):  
Physical Properties ◽  
Augmented Lagrangian ◽  
Equations Of Motion ◽  
Time Integration ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Integration Schemes

This paper addresses practical issues associated with the numerical enforcement of constraints in flexible multibody systems, which are characterized by index-3 differential algebraic equations (DAEs). The need to scale the equations of motion is emphasized; in the proposed approach, they are scaled based on simple physical arguments, and an augmented Lagrangian term is added to the formulation. Time discretization followed by a linearization of the resulting equations leads to a Jacobian matrix that is independent of the time step size, h; hence, the condition number of the Jacobian and error propagation are both O(h0): the numerical solution of index-3 DAEs behaves as in the case of regular ordinary differential equations (ODEs). Since the scaling factor depends on the physical properties of the system, the proposed scaling decreases the dependency of this Jacobian on physical properties, further improving the numerical conditioning of the resulting linearized equations. Because the scaling of the equations is performed before the time and space discretizations, its benefits are reaped for all time integration schemes. The augmented Lagrangian term is shown to be indispensable if the solution of the linearized system of equations is to be performed without pivoting, a requirement for the efficient solution of the sparse system of linear equations. Finally, a number of numerical examples demonstrate the efficiency of the proposed approach to scaling.

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

Simulation of 2-D Dam Break Using Improved Incompressible Smoothed Particle Hydrodynamics Based on Projection Method

2013 ◽  
Vol 390 ◽  
pp. 81-85
Author(s):  
Majid Pourabdian ◽  
Mehran Qate ◽  
Alireza Javareshkian ◽  
Ali Farzbod
Keyword(s):  
Projection Method ◽  
Smoothed Particle Hydrodynamics ◽  
Half Time ◽  
Time Step ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics ◽  
Secondary Velocity ◽  
Subsequent Propagation ◽  
Stability And Accuracy

This paper deals with numerical modeling of water flow which is generated by the break of a dam. The problem is solved by applying a new Incompressible Smoothed Particle Hydrodynamics (ISPH) algorithm based on projection method. The proposed ISPH model has two steps. In the first step, the incompressibility of fluid is maintained regarding to the changes of intermediate and initial particles densities at the first half-time step (stability step). In the second step, by computing the divergence of the intermediate secondary velocity at the second half-time step (accuracy step), the incompressibility is satisfied completely. In fact, by using this method both stability and accuracy are increased. The simulation illustrates the formation and subsequent propagation of a wave over the horizontal plane. It is shown that the model predictions compare well with experimental data.

A PCISPH implementation using distributed multi-GPU acceleration for simulating industrial engineering applications

2020 ◽  
Vol 34 (4) ◽  
pp. 450-464
Author(s):  
Kevin Verma ◽  
Christopher McCabe ◽  
Chong Peng ◽  
Robert Wille
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
High Performance ◽  
Optimization Techniques ◽  
Test Case ◽  
Time Step ◽  
Water Splash ◽  
Particle Hydrodynamics ◽  
Order Of Magnitude ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics

Predictive–corrective incompressible smoothed particle hydrodynamics (PCISPH) is a promising variant of the particle-based fluid modeling technique smoothed particle hydrodynamics (SPH). In PCISPH, a dedication prediction–correction scheme is employed which allows for using a larger time step and thereby outperforms other SPH variants by up to one order of magnitude. However, certain characteristics of the PCISPH lead to severe synchronization problems that, thus far, prevented PCISPH from being applied to industrial scenarios where high performance computing techniques need to leveraged in order to simulate in appropriate resolution. In this work, we are for the first time, presenting a highly accelerated PCISPH implementation which employs a distributed multi-GPU architecture. To that end, dedicated optimization techniques are presented that allow to overcome the drawbacks caused by the algorithmic characteristics of PCISPH. Experimental evaluations on a standard dam break test case and an industrial water splash scenario confirm that PCISPH can be efficiently employed to model real-world scenarios involving a large number of particles.

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