On the Volume Conservation of the Immersed Boundary Method

2012 ◽  
Vol 12 (2) ◽  
pp. 401-432 ◽  
Author(s):  
Boyce E. Griffith
Keyword(s):  
Projection Method ◽  
Projection Methods ◽  
Staggered Grid ◽  
Benchmark Problems ◽  
Immersed Boundary ◽  
Lagrangian Description ◽  
Volume Conservation ◽  
Modest Improvement ◽  
Order Of Magnitude ◽  
Ib Method

AbstractThe immersed boundary (IB) method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid. It is well known that some versions of the IB method can suffer from poor volume conservation. Methods have been introduced to improve the volume-conservation properties of the IB method, but they either have been fairly specialized, or have used complex, nonstandard Eulerian finite-difference discretizations. In this paper, we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method. We consider both collocated and staggered-grid discretization methods. For the tests considered herein, the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods, and in many cases considered in this work, the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes. We also compare the performance of cell-centered schemes that use either exact or approximate projection methods. We find that the volume-conservation properties of approximate projection IB methods depend strongly on the formulation of the projection method. When used with the IB method, we find that pressure-free approximate projection methods can yield extremely poor volume conservation, whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.

A Very Simple Immersed Boundary Method Applied to Three-Dimensional Incompressible Navier-Stokes Solvers Using Staggered Grid

2007 ◽  
Author(s):  
Satoru Yamamoto ◽  
Koichiro Mizutani
Keyword(s):  
Immersed Boundary Method ◽  
Computational Algorithm ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Surface Mesh ◽  
Flow Problems ◽  
Smac Method ◽  
Ib Method

A very simple computational algorithm for solving flows over complex geometries is presented. This algorithm is based on a kind of the Immersed Boundary (IB) Methods. The complex 3D geometries are generated by the 3DCG software as a surface mesh of triangle polygons. A 3D Cartesian grid is used for the flow field. Only the points stuck with grid lines on triangle polygons are detected and flow velocities are modified using the points with the IB method. In this paper, this approach is applied to an incompressible Navier-Stokes solver based on the Simplified Marker and Cell (SMAC) method. Some practical flow problems assuming low Reynolds number are calculated and the results are compared with the experimental and the numerical results.

scholarly journals A numerical study of fish adaption behaviors in complex environments with a deep reinforcement learning and immersed boundary–lattice Boltzmann method

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yi Zhu ◽  
Fang-Bao Tian ◽  
John Young ◽  
James C. Liao ◽  
Joseph C. S. Lai
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Prey Capture ◽  
Numerical Study ◽  
Benchmark Problems ◽  
Immersed Boundary ◽  
Complex Environments ◽  
Fish Model ◽  
Point To Point ◽  
Boltzmann Method

AbstractFish adaption behaviors in complex environments are of great importance in improving the performance of underwater vehicles. This work presents a numerical study of the adaption behaviors of self-propelled fish in complex environments by developing a numerical framework of deep learning and immersed boundary–lattice Boltzmann method (IB–LBM). In this framework, the fish swimming in a viscous incompressible flow is simulated with an IB–LBM which is validated by conducting two benchmark problems including a uniform flow over a stationary cylinder and a self-propelled anguilliform swimming in a quiescent flow. Furthermore, a deep recurrent Q-network (DRQN) is incorporated with the IB–LBM to train the fish model to adapt its motion to optimally achieve a specific task, such as prey capture, rheotaxis and Kármán gaiting. Compared to existing learning models for fish, this work incorporates the fish position, velocity and acceleration into the state space in the DRQN; and it considers the amplitude and frequency action spaces as well as the historical effects. This framework makes use of the high computational efficiency of the IB–LBM which is of crucial importance for the effective coupling with learning algorithms. Applications of the proposed numerical framework in point-to-point swimming in quiescent flow and position holding both in a uniform stream and a Kármán vortex street demonstrate the strategies used to adapt to different situations.

Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhenglun Alan Wei ◽  
Zhongquan Charlie Zheng ◽  
Xiaofan Yang
Keyword(s):  
Porous Media ◽  
Parallel Implementation ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Periodic Array ◽  
Immersed Boundary ◽  
Navier Stokes Equation ◽  
Flow Through ◽  
Ib Method

A parallel implementation of an immersed-boundary (IB) method is presented for low Reynolds number flow simulations in a representative elementary volume (REV) of porous media that are composed of a periodic array of regularly arranged structures. The material of the structure in the REV can be solid (impermeable) or microporous (permeable). Flows both outside and inside the microporous media are computed simultaneously by using an IB method to solve a combination of the Navier–Stokes equation (outside the microporous medium) and the Zwikker–Kosten equation (inside the microporous medium). The numerical simulation is firstly validated using flow through the REVs of impermeable structures, including square rods, circular rods, cubes, and spheres. The resultant pressure gradient over the REVs is compared with analytical solutions of the Ergun equation or Darcy–Forchheimer law. The good agreements demonstrate the validity of the numerical method to simulate the macroscopic flow behavior in porous media. In addition, with the assistance of a scientific parallel computational library, PETSc, good parallel performances are achieved. Finally, the IB method is extended to simulate species transport by coupling with the REV flow simulation. The species sorption behaviors in an REV with impermeable/solid and permeable/microporous materials are then studied.

scholarly journals Study on Fluid-Structure Interaction of Flexible Membrane Structures in Wind-Induced Vibration

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fangjin Sun ◽  
Donghan Zhu ◽  
Tiantian Liu ◽  
Daming Zhang
Keyword(s):  
Projection Method ◽  
Fluid Structure Interaction ◽  
Initial Pressure ◽  
Projection Methods ◽  
Accurate Solution ◽  
Membranous Structure ◽  
Fluid Structure ◽  
Strongly Coupled ◽  
Structure Interaction ◽  
Modified Projection Method

A strongly coupled monolithic method was previously proposed for the computation of wind-induced fluid-structure interaction of flexible membranous structures by the authors. How to obtain the accurate solution is a key issue for the strongly coupled monolithic method. Projection methods are among the commonly used methods for the coupled solution. In the work here, to impose initial pressure boundary conditions implicitly defined in the original momentum equations in classical projection methods when dealing with large-displacement of membranous structures, a modified factor is introduced in corrector step of classical projection methods and a new modified projection method is obtained. The solution procedures of the modified projection method aimed at strongly coupled monolithic equations are given, and the related equations are derived. The proposed method is applied to the computation of a two-dimensional fluid-structure interaction benchmark case and wind-induced fluid-structure interaction of a three-dimensional flexible membranous structure. The performance and efficiency of the modified projection method are evaluated. The results show that the modified projection methods are valid in the computation of wind-induced fluid-structure interaction of flexible membranous structures, with higher accuracy and efficiency compared with traditional methods. The modified value has little effects on the computation results whereas iteration times has significant effects. Computation accuracy can be improved greatly by increasing iteration times with less increase in computation time and little effects on stability with the modified projection method.

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

Simulation of Jet Issued Into Two-Layer Density-Stratified Fluid by Vortex in Cell Method Combined With Immersed Boundary Method

2015 ◽  
Author(s):  
Isao Aozasa ◽  
Tomomi Uchiyama
Keyword(s):  
Immersed Boundary Method ◽  
Water Solution ◽  
Simulation Method ◽  
Stratified Fluid ◽  
Immersed Boundary ◽  
Layer Density ◽  
Jet Behavior ◽  
Lower Fluid ◽  
Ib Method ◽  
Present Simulation

Jet flow issued into two-layer density-stratified fluid in a cylindrical tank is numerically simulated. Vortex in cell (VIC) method combined with an Immersed Boundary (IB) method, which is presented by the current authors, is applied to the simulation. The upper and lower fluids are water and a NaCl-water solution, respectively, and the lower fluid is issued vertically upward from a nozzle on the bottom of the tank. The Reynolds number Re defined by the jet velocity and the nozzle diameter ranges from 95 to 1188, and the mass concentration of the NaCl-water solution C0 is set at 0 and 0.02. The simulation highlights that the jet behavior relative to the density interface and the resultant mixing phenomena depend on Re. Such simulated results are confirmed to agree well with the experimentally visualized ones, demonstrating the validity of the present simulation method.

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

2019 ◽  
Vol 37 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Xiaosong Du ◽  
Leifur Leifsson
Keyword(s):  
Polynomial Chaos ◽  
State Of The Art ◽  
Uncertainty Propagation ◽  
Kriging Model ◽  
Probability Of Detection ◽  
Kriging Interpolation ◽  
Benchmark Problems ◽  
Content Type ◽  
Order Of Magnitude ◽  
Polynomial Chaos Expansions

Purpose Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models. Design/methodology/approach In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels. Findings To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent. Originality/value The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

An Aid to Learn Computational Fluid Dynamics: Immersed-Boundary-Based Simulation of 2D Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
Sungsu Lee ◽  
Kyung-Soo Yang ◽  
Jong-Yeon Hwang
Keyword(s):  
Complex Geometry ◽  
Mass Conservation ◽  
Computational Method ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equation ◽  
Finite Volume Approach

Development of geometry-independent computational method and educational codes for simulation of 2D flows around objects of complex geometry is presented. Referred as immersed boundary method, it introduces virtual forcing to governing equations to represent the effect of physical boundaries. The present method is based on a finite-volume approach on a staggered grid with a fractional-step method to solve Navier-Stokes equation and continuity equation. Both momentum and mass forcings are introduced on and inside the object to satisfy no-slip condition and mass conservation. Since Cartesian grid lines in general do not coincide with the immersed boundaries, several interpolation schemes are employed. Several examples are simulated using the method presented in this study and the results agree well with other results. Both user-friendly preprocessor with GUI and FORTRAN-based solver are open to the public for educational purposes.

A Lattice Boltzmann-Immersed Boundary-Finite Element Method for Nonlinear Fluid–Solid Interaction Simulation with Moving Objects

2018 ◽  
Vol 15 (07) ◽  
pp. 1850063 ◽  
Author(s):  
Chunlin Gong ◽  
Zhe Fang ◽  
Gang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lattice Boltzmann ◽  
Moving Objects ◽  
Moving Boundaries ◽  
Immersed Boundary ◽  
Nonlinear Fem ◽  
Ib Method ◽  
Nonlinear Fluid ◽  
Element Method

A nonlinear finite element method (FEM) was introduced into the immersed boundary (IB) — lattice Boltzmann method (LBM) framework to simulate the nonlinear fluid–solid interactions for moving deformable objects in incompressible fluid flow. The fluid motion is obtained by solving the discrete lattice Boltzmann equation, the moving boundaries of the solids are handled by the IB method, and the nonlinear dynamics of the deforming/moving objects are calculated by nonlinear FEM solvers in which the structural nodes are also set as Lagrangian markers to track the moving boundaries of the structures in IB method. The simulation results indicate that the proposed IB-LBM-FEM simulation framework not only satisfies the nonslip boundary condition well at the boundary points, but also has better accuracy for capturing nonlinearity because of its mature nonlinear FEM solver.

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