Smoothed Profile Method for Particulate Two-Phase Flow

2008 ◽  
Author(s):  
Xian Luo ◽  
Martin R. Maxey ◽  
George E. Karniadakis
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Integration Scheme ◽  
Force Density ◽  
Step Size ◽  
Time Step ◽  
Element Discretization ◽  
Profile Method ◽  
Time Step Size ◽  
Smoothed Profile Method

We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

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.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

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 Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

2013 ◽  
Vol 13 (2) ◽  
pp. 386-410 ◽  
Author(s):  
Björn Sjögreen ◽  
Jeffrey W. Banks
Keyword(s):  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Linear Equations ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Computational Domain ◽  
Interface Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

AbstractWe consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjögreen in [8] as a special case.

Numerical Study on the Effect of a Volute on Surge Phenomena in a Centrifugal Compressor

2016 ◽  
Author(s):  
S. H. Jeon ◽  
D. H. Hwang ◽  
J. H. Park ◽  
C. H. Kim ◽  
J. H. Baek ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Flow Instability ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Unstable Flow ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Blade Passing Frequency

Numerical investigation of the effect of the volute on stall flow phenomenon is presented by solving three-dimensional Reynolds-averaged compressible Navier-Stokes equations. Two different configurations of a centrifugal compressor were used to compare their performance: One is an original centrifugal compressor which is composed of impeller, splitter, vaned diffuser and a volute and the other is the one without a volute. Steady calculations were performed to predict aerodynamic performance in terms of the pressure ratio, efficiency and mass flow rate. The results show that the operating range of the compressor with a volute is narrower than that of the compressor without a volute. This can be interpreted that flow instability is strongly influenced by the tongue of a volute which is highly asymmetric. Unsteady calculations were also performed with a time-step size of 38μs corresponding to a pitch angle of 5 degrees at the given rotational speed. The flow characteristics for two configurations are analyzed and compared at various instantaneous times showing unsteady dynamic features. Based on the unsteady flow simulation, fast Fourier transform at several discrete points in semi-vaneless space was performed at peak efficiency and near surge point in order to illustrate the unstable flow physics in both configurations. It is found that the blade passing frequency is dominant, indicating that diffuser passages have a periodicity of 40 degrees due to the rotational blades. Besides blade passing frequency, there were several noticeable frequencies which affect the instability of the whole system. Those frequencies in both configurations are compared and analyzed in various aspects.

Next Generation Safety Analysis Methods for SFRs—(4) Development of a Computational Framework on Fluid-Solid Mixture Flow Simulations for the COMPASS Code

2009 ◽  
Author(s):  
Shuai Zhang ◽  
Koji Morita ◽  
Noriyuki Shirakawa ◽  
Yuichi Yamamoto
Keyword(s):  
Distinct Element ◽  
Integration Scheme ◽  
Step Size ◽  
Time Step ◽  
Mixture Flow ◽  
Computational Framework ◽  
Mps Method ◽  
Time Step Size ◽  
Flow Simulations ◽  
Solid Mixture

The COMPASS code is designed based on the moving particle semi-implicit (MPS) method to simulate various complex mesoscale phenomena relevant to core disruptive accidents (CDAs) of sodium-cooled fast reactors (SFRs). The MPS method, which is a fully Lagrangian method, can be extended for fluid-solid mixture flow simulations in a straightforward approach. In this study, a computational framework for fluid-solid mixture flow simulations was developed for the COMPASS code. In the present framework, the passively moving solid (PMS) model, which is originally proposed to describe the motion of a rigid body in a fluid, used to simulate hydrodynamic interactions between fluid and solids. In addition, mechanical interactions between solids were modeled by the distinct element method (DEM). Since the typical time step size in DEM calculation, which uses an explicit time integration scheme, is much smaller than that in MPS calculation, a multi-time-step algorithm was introduced to couple these two calculations. In order to verify the proposed computational framework for fluid-solid mixture flow simulations, a series of experiments of water-dam break with multiple solid rods was simulated using the COMPASS code. It was found that simulations considering only fluid-solid interactions using the PMS model can not reasonably represent typical behaviors of solid rods observed in the experiments. However, results of simulations taking account of solid-solid interactions using DEM as well as fluid-solid ones were in good agreement with experimental observations. It was demonstrated that the present computational framework enhances the capability of the COMPASS code for mesoscale simulations of fluid-solid mixture flow phenomena relevant to CDAs of SFRs. To improve the computational efficiency for fluid-solid mixture flow simulations, it will be necessary to optimize the time step size used in DEM calculations by adjusting DEM parameters based on additional experiments and numerical tests.

Modeling the damped dynamic behavior of a flexible pendulum

2019 ◽  
Vol 54 (2) ◽  
pp. 116-129 ◽  
Author(s):  
Roberto Ortega ◽  
Geraldine Farías ◽  
Marcela Cruchaga ◽  
Matías Rivero ◽  
Mariano Vázquez ◽  
...  
Keyword(s):  
High Speed ◽  
Time Integration ◽  
Integration Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Rayleigh Damping ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Damping Model

The focus of this work is on the computational modeling of a pendulum made of a hyperelastic material and the corresponding experimental validation with the aim of contributing to the study of a material commonly used in seismic absorber devices. From the proposed dynamics experiment, the motion of the pendulum is recorded using a high-speed camera. The evolution of the pendulum’s positions is recovered using a capturing motion technique by tracking markers. The simulation of the problem is developed in the framework of a parallel multi-physics code. Particular emphasis is placed on the analysis of the Newmark integration scheme and the use of Rayleigh damping model. In particular, the time step size effect is analyzed. A strong time step size dependency is obtained for dissipative time integration schemes, while the Rayleigh damping formulation without time integration dissipation shows time step–independent results when convergence is achieved.

scholarly journals Multi-Degree of Freedom Propeller Force Models Based on a Neural Network and Regression

2020 ◽  
Vol 8 (2) ◽  
pp. 89 ◽  
Author(s):  
Bradford Knight ◽  
Kevin Maki
Keyword(s):  
Neural Network ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Open Water ◽  
Small Time ◽  
Training Data ◽  
Step Size ◽  
Time Step ◽  
Neural Network Approach ◽  
Time Step Size

Accurate and efficient prediction of the forces on a propeller is critical for analyzing a maneuvering vessel with numerical methods. CFD methods like RANS, LES, or DES can accurately predict the propeller forces, but are computationally expensive due to the need for added mesh discretization around the propeller as well as the requisite small time-step size. One way of mitigating the expense of modeling a maneuvering vessel with CFD is to apply the propeller force as a body force term in the Navier–Stokes equations and to apply the force to the equations of motion. The applied propeller force should be determined with minimal expense and good accuracy. This paper examines and compares nonlinear regression and neural network predictions of the thrust, torque, and side force of a propeller both in open water and in the behind condition. The methods are trained and tested with RANS CFD simulations. The neural network approach is shown to be more accurate and requires less training data than the regression technique.

On an Improved Time Integration Scheme for Stiff Constitutive Models of Inelastic Deformation

1985 ◽  
Vol 107 (4) ◽  
pp. 282-285 ◽  
Author(s):  
Vinod Banthia ◽  
Subrata Mukherjee
Keyword(s):  
Strain Rate ◽  
Inelastic Deformation ◽  
Time Integration ◽  
Constitutive Models ◽  
Size Control ◽  
Integration Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Step Size Control

For the time-integration of stiff constitutive models of inelastic deformation, the explicit (one step Euler) integration scheme can be used provided the time step size is closely monitored and controlled. The time step size control scheme based on prescribed error bounds is of limited use because it requires an a priori estimate of the maximum nonelastic strain rate for the selection of a proper error bound. In this paper, a new scheme for time-step size control is presented. This scheme automatically scales the time-step size by the maximum nonelastic strain rate. That the new scheme is superior to the old one is evident from the results of the various problems presented here.

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