Pressure Correction Method for Simulating Solid-Fluid Mixture Flow

2011 ◽  
Author(s):  
San-Yih Lin ◽  
Ya-Hsien Chin ◽  
Yi-Cheng Chen
Keyword(s):  
Particle Interaction ◽  
Three Dimensional ◽  
Correction Method ◽  
Immersed Boundary ◽  
Time Step ◽  
Fluid Mixture ◽  
Mixture Flow ◽  
Pressure Correction ◽  
Step Algorithm ◽  
Solid Bodies

A pressure correction method is developed to simulate fluid-particle interaction flows. In this Paper, the three-dimensional solid-fluid mixture flows are investigated. The pressure corrected method coupled with the direct-forcing immersed boundary (IB) and the volume of fluid (VOF) methods is used to simulate the mixture flows. A discrete element method (DEM) together with a multi-time-step algorithm is introduced into the pressure correction method to calculate the forces and torques between solid bodies and between solid bodies and walls. As a demonstration of the efficient and capabilities of the present method, four test cases are simulated. They include sedimentation of one spherical particle in an enclosure, collapse of six solid-cylinder layers, two-dimensional solid-fluid mixture flow, and three-dimensional solid-fluid mixture flow.

Three-Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 469-476 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Correction Method ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Blade Passage ◽  
Time Marching ◽  
Viscous Solutions

A three-dimensional nonlinear time-marching method of solving the thin-layer Navier–Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the four-stage Runge–Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The three-dimensional unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established three-dimensional semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present three-dimensional unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable three-dimensional viscous flow features. The feasibility of solving the simplified thin-layer Navier–Stokes solver for oscillating blade flows at practical conditions is demonstrated.

A Sharp-Interface Immersed Boundary Method for Simulating Incompressible Flows with Arbitrarily Deforming Smooth Boundaries

2017 ◽  
Vol 15 (01) ◽  
pp. 1750080 ◽  
Author(s):  
Zuo Cui ◽  
Zixuan Yang ◽  
Hong-Zhou Jiang ◽  
Wei-Xi Huang ◽  
Lian Shen
Keyword(s):  
Incompressible Flows ◽  
Deformable Body ◽  
Fluid Flows ◽  
Sharp Interface ◽  
Immersed Boundary ◽  
Time Step ◽  
Fluid Forces ◽  
Solid Bodies ◽  
Ib Method ◽  
Moving Bodies

We develop a sharp interface immersed boundary (IB) method to simulate the interactions between fluid flows and deformable moving bodies. Fluid–solid interfaces are captured using a level-set (LS) function, which is updated at every time step by a reinitialization procedure. Motions of solid bodies are dynamically coupled with fluid flows by calculating the fluid forces exerted on solid bodies. The accuracy and robustness of the LS-based IB method are tested systematically in the context of several benchmark cases and self-propelled fish swimming. The effects of computational parameters on the accuracy of deformable body capturing are analyzed. It is found that the algorithm performs well in simulating the flow motions surrounding the deforming and moving bodies.

scholarly journals Consistent Velocity–Pressure Coupling for Second-Order L2-Penalty and Direct-Forcing Methods

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 92
Author(s):  
Arthur Sarthou ◽  
Stéphane Vincent ◽  
Jean-Paul Caltagirone
Keyword(s):  
Stokes Equations ◽  
Correction Method ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Immersed Boundary ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Numerical Instabilities ◽  
Pressure Projection ◽  
Velocity Pressure

The present work studies the interactions between fictitious-domain methods on structured grids and velocity–pressure coupling for the resolution of the Navier–Stokes equations. The pressure-correction approaches are widely used in this context but the corrector step is generally not modified consistently to take into account the fictitious domain. A consistent modification of the pressure-projection for a high-order penalty (or penalization) method close to the Ikeno–Kajishima modification for the Immersed Boundary Method is presented here. Compared to the first-order correction required for the L 2 -penalty methods, the small values of the penalty parameters do not lead to numerical instabilities in solving the Poisson equation. A comparison of the corrected rotational pressure-correction method with the augmented Lagrangian approach which does not require a correction is carried out.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

A three-dimensional immersed boundary method based on an algebraic forcing-point-searching scheme for water impact problems

2021 ◽  
Vol 233 ◽  
pp. 109189
Author(s):  
Bin Yan ◽  
Wei Bai ◽  
Sheng-Chao Jiang ◽  
Peiwen Cong ◽  
Dezhi Ning ◽  
...  
Keyword(s):  
Immersed Boundary Method ◽  
Three Dimensional ◽  
Immersed Boundary ◽  
Water Impact ◽  
Boundary Method ◽  
Impact Problems

scholarly journals 3D monitoring of the surface slippage effect on micro-particle sedimentation by digital holographic microscopy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Majid Panahi ◽  
Ramin Jamali ◽  
Vahideh Farzam Rad ◽  
Mojtaba Khorasani ◽  
Ahamd Darudi ◽  
...  
Keyword(s):  
Slip Length ◽  
Particle Interaction ◽  
Three Dimensional ◽  
Digital Holographic Microscopy ◽  
Particle Sedimentation ◽  
Micro Particles ◽  
Slippage Effect ◽  
Holographic Microscopy ◽  
3D Information ◽  
Experimental Findings

AbstractIn several phenomena in biology and industry, it is required to understand the comprehensive behavior of sedimenting micro-particles in fluids. Here, we use the numerical refocusing feature of digital holographic microscopy (DHM) to investigate the slippage effect on micro-particle sedimentation near a flat wall. DHM provides quantitative phase contrast and three-dimensional (3D) imaging in arbitrary time scales, which suggests it as an elegant approach to investigate various phenomena, including dynamic behavior of colloids. 3D information is obtained by post-processing of the recorded digital holograms. Through analysis of 3D trajectories and velocities of multiple sedimenting micro-particles, we show that proximity to flat walls of higher slip lengths causes faster sedimentation. The effect depends on the ratio of the particle size to (1) the slip length and (2) its distance to the wall. We corroborate our experimental findings by a theoretical model which considers both the proximity and the particle interaction to a wall of different hydrophobicity in the hydrodynamic forces.

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