COMPUTATIONAL SIMULATION OF FLUID FLOW OVER A TRIANGULAR STEP USING IMMERSED BOUNDARY METHOD

In the literature immersed boundary methods are employed tosimulate complex flows around moving arbitrary bodies without thenecessity of remeshing. These methods employ a regular Eulerian meshto simulate the fluid flow and a Lagrangian representation of theboundary of the bodies. The two representations can be coupled throughan immersed boundary condition constraining the fluid to exactlyfollow the boundary of the bodies (immersed boundaries). Typicallysuch methods suffer from accuracy problems, that arise from spuriousmass fluxes over the immersed boundary (IB), pressure boundaryconditions or high density ratios. The mirroring IB method Mark(2008); Mark and van Wachem (2008) resolves these problems by ensuringzero mass flux over the IB instead of employing a pressure boundarycondition. In this work the mirroring IB method together with a hybridIB condition are implemented and validated in IBOFLOW. IBOFLOW is anincompressible finite-volume based fluid flow solver. TheNavier-Stokes' equations are coupled with the SIMPLEC Doormaal andRaithby (1984) method and discretized on a Cartesian octree grid thatcan be dynamically refined and coarsened, enabling grid refinement tofollow moving bodies. The variables are stored in a co-locatedconfiguration and pressure weighted flux interpolation Rhie and Chow(1983) is employed to prevent pressure oscillations. In theimplemented IB method the immersed bodies are represented by ananalytical description or by a triangulation. The method models thepresence of the bodies inside the fluid by an implicitly formulated IBcondition, which constrains the fluid velocity to the boundaryvelocity with second-order accuracy. The original mirroring IBcondition mirrors the velocity field over the local IB and the hybridIB condition mirrors and extrapolates the fluid velocity onto the IB.These IB conditions generate a fictitious velocity field inside thebodies, which is excluded in the continuity equation to ensure zeromass flux over the boundary. The fluid flow over an immersed sphere issimulated to validate and compare the different IB conditions. Thesimulated drag force is compared to experimental findings withexcellent agreement and a detailed convergence study of the error ofthe fluid velocity integrated over the immersed boundary is performedto show the strictly second-order accuracy of the implemented IBconditions. It is shown that the error is reduced with the hybrid IBcondition compared to the original mirroring IB condition. Inaddition, a sedimenting sphere with a moving grid refinement issimulated to validate the hybrid method and show the potential of thedynamic octree grid.

Composite B-spline regularized delta functions for the immersed boundary method: Divergence-free interpolation and gradient-preserving force spreading.

An immersed boundary formulation incorporating a two-layer wall model approach for RANS simulations with complex geometry

In the past decade a large degree of advancement has been made in CFD labs worldwide, towards the development of Immersed Boundary (IB) CFD methods. The IB method belongs to a new class of numerical methods sometime called mesh-less methods, as no standard meshes that conform to the geometry (or body) need to be generated. The discrete points where the calculation is performed can be freely distributed in the computational domain without great concern for the position of the geometry. The geometry is immersed into a Cartesian grid and the methodology accounts for the effects of the presence of the body in the flow field. The IB method therefore frees up the user from the time consuming and often complicated need for meshing. Plenty of proofs of accuracy and validations are presented yearly at the most prestigious CFD conferences and are available on the internet. Oil and Gas CFD applications are concerned with a variety of internal flow problems. Most of those problems present geometrical complexities, valves for instance, that make a standard body-fitted generation of good quality meshes almost an impossible task. And bad inputs, such as low quality meshes, always determine bad outputs, low quality results. In this paper the KARALIT CFD code based on a class of IB methodology akin to ghost cell methods, is applied to a class of applications encountered often in oil and gas plants, namely a pipeline connecting an arbitrary number of valves, or other devices. While complex valves and devices do make the standard body-fitted approach extremely tedious and difficult, on the other side pipelines are naturally and easily modeled using standard body-fitted cylindrical meshes. The hybrid CFD approach presented will show an automatic implementation of mixed type domain: pipes cylindrical body-fitted meshes are automatically generated by the method and automatically connected to the devices which are treated with the IB method. Examples of lines with arbitrary number of devices will be shown. Result and key performance parameters are provided from the IB CFD calculations and key conclusions about the line characteristic are drawn.

SUMMARYIn this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high‐order weighted‐essentially non‐oscillatory (WENO) scheme to simulate fluid–solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well‐documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface‐to‐volume ratio of the obstacle matrix. It is shown that the configuration with higher surface‐to‐volume ratio produces more post‐shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re → ∞ . The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237–256). Copyright © 2011 John Wiley & Sons, Ltd.

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the structure and Eulerian variables to describe the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methods require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. These tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100--1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50--200 times more efficient than the explicit method.

Hydrodynamic simulations of storm-surge waves on coastal structures are essential for coastal areas in predicting wave and flood damages. In a large scale regional model, the coastal structures, such as networks of coastal highways, floodgates and levees, are often complex in shapes. In addition, the width of those structures are smaller in size compared to the grid sizes which in the ranges of 10s to 100s meters. Therefore, in hydrodynamic simulations, it is not possible to use body fitted mesh to conform with the shapes of those networks due to the complicated shapes, and it is very expensive to resolve these small scale structures with very fine grid resolutions. The Immersed Boundary Method (IBM) allows for overcoming these difficulties with an accurate but less expensive way. Since the structures were represented by immersed boundary (IB) points which do not have to be collocated with grid points, complicates shapes structures and the structures smaller than grid resolutions can be realized, and simple Cartesian grids can be utilized without sacrificing accuracy. In a previous study by the authors, an infinite height floodgate/levee structure has been implemented using an IBM which the IB force terms were added in both u and v equations while no IB force term in z (water-elevation) equation. In this study, the height effect was added to the previous developed model. It is worth mentioning that the background flow model is a 2-D depth-averaged shallow water flow model, and the height effect is not implemented by a 3-D mesh. Instead, it is implemented by adding the IB force to the water-elevation equation. The feedback-force type of IBM was used in this study because of its superior performance on this type of simulations compared to the counterpart direct-forcing IBM as shown in the author’s previous publication. In this study, the CaFunwave package was used as the background flow solver, and the IB implementation was written into an separate function incorporated to the package. The equations solved in CaFunwave are the fully nonlinear Boussinesq-type equations, which are capable of modeling of near-shore hydrodynamics. The original model of CaFunwave is FUNWAVE-TVD. In this paper, constant height and non-constant height floodgates/levees were implemented in the simulations. Non-constant height represents broken floodgate/levee situations that parts of the structure are collapsed. The results of one constant-height gate simulation were compared to the results of a simulation that a finite height gate that was constructed directly from the topography data for validation. The floodgate/levee height and shape effects on the flows and waves were revealed from the simulation results.

ABSTRACTIn the present study, a high‐order hybrid compact‐weighted essentially non‐oscillatory (WENO) scheme is applied in conjunction with the immersed boundary method for efficiently computing compressible inviscid flows around two‐dimensional solid bodies. For this aim, the two‐dimensional unsteady compressible Euler equations written in the conservative form are considered and they are discretized in the space by using the hybrid fifth‐order compact‐WENO (CW) finite‐difference scheme and the third‐order explicit TVD Runge–Kutta scheme in the time. The solid bodies are appropriately imposed to the computational domain by using the immersed boundary method as an effective procedure in modeling the complex configurations without the difficulties usually encountered in generating the computational grid over such problems. Different test cases are simulated by applying the hybrid CW immersed boundary method and the present results are compared with those of available finite‐difference immersed boundary methods. To further assess the solution method applied, the present results are also obtained by the high‐order WENO immersed boundary scheme, and these two high‐order accurate solution procedures are thoroughly compared with each other. The main advantage of using the hybrid CW finite‐difference immersed boundary method applied here is that it provides a more accurate solution with lower computational cost in comparison with the traditional and high‐order WENO finite‐difference immersed boundary methods. It is shown that the solution procedure based on the hybrid CW scheme implemented via the immersed boundary method has still reasonable shock‐capturing features and it can effectively be applied for accurately computing the compressible inviscid flows with the complicated flow structures and the embedded discontinuities such as the shocks over the complicated geometries.

Numerical study on hydrodynamics for a non-sinusoidal forced oscillating hydrofoil based on an immersed boundary method

Pore-scale modeling of flow in porous and fractured media is a first key step to provide a firm knowledge basis for effective aquifer management practices in environmental applications or to improved reservoir performance in the oil and gas field. We present a performance comparison of two numerical approaches for the pore-scale simulation of fully saturated flow in natural porous media. Real samples of rocks at the millimeter scale whose complex pore space geometry is reconstructed through X-ray computer tomography are considered. The governing flow equation in the system are solved by employing a Body-Fitted (BF) grid and an Immersed Boundary (IB) method, as respectively embedded in FLUENT and EULAG (Prusa et al., 2008) software environments. The BF technique allows solving the flow problem within the real pore space and is widely adopted in computational fluid dynamics since it allows to fit complex geometries while preserving accuracy, up to a certain level of detail. The method is associated with some limitations in the presence of extremely complex geometrical setting of the kind encountered in natural or reconstructed micro scale porous systems, mainly due to the time-demanding mesh generation stage. On the other hand, IB methods can take full advantage of uniform Cartesian grid implementations describing both the fluid and solid regions in the domain. Grain size distributions are modeled by considering an additional forcing term in the governing flow equation. This term inhibits Sow through the solid matrix and hence acts to enforce the no-slip condition at solid walls. The effectiveness of such term, i.e., its ability to prevent mass flow rate within the solid domain, is controlled by a parameter, a, which is directly related to the characteristic time scale of the forcing action. First, the performance of each model is analyzed separately on the same rock samples. Grid dependence is tested for the BF method upon comparing simulations at three different levels of resolution. A detailed sensitivity analysis is performed to assess the role of the parameter α in the IB method simulations. Finally, the two models are compared in terms of resulting flow fields, mass-conservation capability, hydraulic conductivity estimates and computational resources requirement.

The objective of this brief review is to showcase recent applications of sharp-interface immersed boundary (IB) method to computationally challenging problems in fluid–structure interaction (FSI). The sharp-interface IB method is briefly reviewed and a scheme to strongly couple the flow and structural solver is discussed. The following applications have been discussed. First, the vortex-induced vibration of a cylinder has been presented. Second, FSI benchmarks of an elastic and a viscoelastic splitter attached on a cylinder involving large-scale flow-induced deformation have been presented. Third, numerical simulations of a FSI benchmark in a heated channel, demonstrating augmentation in convective heat transfer, have been reviewed. Finally, the flow-induced deformation of a thin elastic plate due to blast loading has been presented. In all of these FSI problems, the IB method has been successfully employed to simulate the coupled fluid and structural dynamics.

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.

The Interpolated Bounce-Back (IBB) method and Immersed Boundary (IB) method are compared for fluid-solid boundary conditions in the Lattice Boltzmann Equation (LBE) in terms of their numerical accuracy and computational efficiency. We carry out simulations for the flow past a circular cylinder asymmetrically placed in the channel in two dimensions with the Reynolds number Re = 20 and 100, corresponding to steady and unsteady flows, respectively. The results obtained by the LBE method are compared with the existing data. We observe that the LBE with either the IBB or IB methods for the no-slip boundary conditions exhibits a second-order rate of convergence. While the computational cost for both methods are comparable, the interpolated bounce-back method is more accurate than the immersed-boundary method with the same mesh size. Consequently the IBB method is more efficient computationally, while the IB method is easier to implement.

Image-based immersed boundary model of the aortic root

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.