Ghost-cell Immersed Boundary Method Research Articles

On wave-current interaction with a horizontal cylinder near free surface by a fourth-order-accurate finite volume compact solver

We present a numerical solver for dealing with the problem of wave-current interaction with a horizontal cylinder near free surface. The solver solves the filtered Navier-Stokes equations which are discretized using a fourth-order-accurate compact finite volume scheme on a collocated grid. The turbulence effect is modelled by a subgrid-scale model using a large eddy simulation, and the free surface and the cylinder are modelled by a volume of fluid method and a ghost cell immersed boundary method. The pressure-velocity coupling is ensured via a momentum interpolation method. We obtain the hydrodynamic force and its spectra characteristics, dynamic pressure distribution, streamline topology and vorticity patterns with different immersed depths under uniform currents, regular waves and wave-current flows. Validation is performed by comparing the calculated hydrodynamic force with the measured data within one wave period. The results show that the position of vortex shedding and dissipation is different for the cases under different immersed depth in regular waves and wave-current flows. The dynamic pressure around the cylinder as the force reaches its peak value changes with immersed depth. The value and phase of the force are sensitive to immersed depth.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

Coupling of multicomponent transport models in particle-resolved fluid-solid simulations

An accurate and self-consistent methodology for mass transport of multi-component mixtures in multi phase media is a necessity for a proper description of complex physical and chemical processes in reactors such as catalytic packed beds. In this regard, a novel methodology has been developed to describe and couple underlying transport phenomena in fluid and porous media as well as at the solid-fluid interface. The methodology is symmetric as it treats all components in a mixture equally. The Maxwell-Stefan equations are symmetrically formulated, discretized conservatively and coupled with a compressible flow solver for the fluid part. The Dusty Gas Model is applied inside porous media by developing a self-consistent and robust numerical formulation. A ghost-cell Immersed Boundary Method is used to capture the physics at the solid-fluid interface with the implementation of a novel symmetric non-singular mass flux formulation. Several test cases are established to demonstrate the accuracy and robustness of the newly developed symmetric methodology in this paper. These test cases can be used as benchmark for the future development of symmetric methodologies for multicomponent systems in multi phase media.

A novel high-fidelity ghost-cell immersed boundary method for the Cartesian grid and its applications

A novel high-fidelity ghost-cell immersed boundary method for the Cartesian grid and its applications

Direct numerical simulations of polypropylene gasification in supercritical water

In order to reduce environmental pollution by plastic wastes, supercritical water gasification (SCWG) appears as a promising technology. The present study investigates the SCWG process of polypropylene (PP) plastic waste using particle-resolved direct numerical simulations (PR-DNS). A directional ghost-cell immersed boundary method has been used to solve the reacting boundary condition, including detailed molecular diffusion models. To validate the procedure, SCWG of a coal particle has been first investigated as a benchmark, analyzing in detail interphase momentum and heat and mass transfer, and chemical reactions are analyzed. Surface reactions and the resulting Stefan flow expand the boundary layer around the particle, impacting the efficiency of heat and mass transfer. Adding then a suitable reaction mechanism, SCWG of PP plastic wastes leading to combustible gases is analyzed by PR-DNS and found to be very efficient. The gasification temperature is an important parameter to control SCWG efficiency. To the authors' knowledge, this is the first PR-DNS study investigating the SCWG process for plastic wastes, and it provides interesting information regarding transfer processes and their limitations.

A CIP-based numerical simulation of wave interaction with a fluid-filled membrane submerged breakwater

This study proposes an CIP (Constraint Interpolation Profile) viscous flow model that couples the Finite Element Method for structural deformation, to investigate the wave interaction with a fluid-filled membrane submerged breakwater. A modified ghost-cell immersed boundary method is adopted to achieve an accurate simulation of the fluid-structure interaction. After validation by published experimental data, the model is used to study the interaction between regular waves and a fluid-filled membrane submerged breakwater. The excess internal pressure, vorticity field, elastic modulus and structural responses are analyzed. The results show that, in lower excess internal pressure, the wave reflection, vortex shedding and energy dissipation are more significant. Besides, through the analysis of displacement and velocity distribution, three different vibration modes of the membrane structure are identified at different wave frequencies.

Fully resolved direct numerical simulation of single coal particle gasification in supercritical water

Supercritical water gasification is a promising technology in the context of carbon neutrality, since it converts coal into hydrogen and easily-captured CO2. A fully resolved direct numerical simulation of single particle gasification in supercritical water is conducted in this paper in order to investigate process details at particle scale. To handle the shrinking reactive particle, a directional ghost-cell immersed boundary method is used with a general Robin-type boundary condition at the interface. Detailed flow field and interphase heat/mass transfer near the reactive coal particle are revealed and compared with standard non-reactive cases – used for validation. They are found to be significantly affected by the combined effect of the reaction-induced Stefan flow, particle shrinking, species generation or destruction, and reaction heat release. The chemical processes are then studied with special attention on the gas-phase reaction time-scale. This study delivers a detailed understanding of coal particle gasification in supercritical water, and provides a first successful test of efficient numerical methods needed for large-scale supercritical water gasification simulations.

A directional ghost-cell immersed boundary method for low Mach number reacting flows with interphase heat and mass transfer

This paper presents a directional ghost-cell immersed boundary method for low Mach number reacting flows with general boundary conditions, extending the approach described in Chi et al. (2020) [17]. The method employs locally directional schemes for ghost value reconstruction and utilization along each discretization direction. In this manner, the boundary condition can be naturally imposed on the boundary intersection point along each coordinate direction, allowing an easy and straightforward implementation of complex boundary conditions. Using Taylor series approximation of fluid points near the immersed boundary, the boundary variable and its gradient governed by arbitrary boundary condition can be implicitly involved, leading to a reliable polynomial extrapolation for the ghost values. In this way, Dirichlet, Neumann and Robin boundary conditions are implemented for general variables with formally second-order accuracy. For reacting gas-solid flow with surface reactions, the reaction-related coefficients in Robin boundary condition lead to a complex implementation in conventional IBM techniques, while the present directional framework leads to a straightforward algorithm while preserving accuracy. The proposed method has been checked by a series of test cases with different boundary conditions, including basic flow, heat and species transport, Stefan problem, and finally two practical applications involving heat and mass transfer. The local accuracy of all boundary conditions exhibits nearly second-order convergence, as expected. While only a single solid object is considered in this first work, the same method can be simply extended to multiple objects of arbitrary shape, leading to fully resolved simulation of reactive particle-laden flows.

Fluid-structure interaction simulations of the ASPIRE SR01 supersonic parachute flight test

High-fidelity fluid-structure interaction (FSI) simulations of the ASPIRE SR01 supersonic parachute flight test are performed through the loose coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD) solvers. The CFD solver employs a Cartesian adaptive mesh refinement (AMR) grid paradigm with a ghost cell immersed boundary method to represent arbitrarily complex geometries, and the CSD solver uses MITC3 triangular shell and Timoshenko beam elements to discretize the parachute canopy and suspension lines. The CFD resolution required to capture the deficit of the dynamic pressure in the wake of the ASPIRE payload and the aerodynamic drag on the parachute canopy is systematically studied via grid refinement study before FSI simulations are conducted. FSI simulations presented consider the inflation of an initially folded parachute canopy in freestream conditions matching the line stretch event during the ASPIRE SR01 flight test. The total pull force at the instance of peak loading is predicted to within 10% of the flight test data. The sensitivity of the total pull force and canopy projected area to the grid resolution in the CFD and CSD domains is systematically studied via another grid refinement study, and grid convergence with respect to the CFD domain resolution is demonstrated. The pull force vs time curve predicted by each CFD and CSD grid resolution varies by less than 1% indicating a high degree of repeatability and low grid-related uncertainty. Remaining differences in the qualitative behavior of the pull force curve and quantitative difference in the peak pull force are thus determined to stem from modeling errors such as the lack of deceleration, and different initial parachute and flow states in the FSI simulations compared to the flight test.

A second-order-accurate immersed boundary ghost-cell method with hybrid reconstruction for compressible flow simulations

This study presents an improved ghost-cell immersed boundary method for geometrically complex boundaries in compressible flow simulations. A bilinearly complete extrapolation scheme is developed for the reconstruction of the ghost-cell. The second-order accuracy of the improved ghost-cell method (GCM) is shown in unit test cases and is also theoretically proven. A hybrid GCM based on both baseline GCM and improved GCM is proposed and constructed. The hybrid GCM applied in compressible flow is validated against five test cases: (a) Stationary rotating vortex, (b) Prandtl–Meyer expansion flow, (c) Double Mach reflection, (d) Moving-shock/obstacle interaction, (e) Blunt body shock-induced combustion. This paper provides a comprehensive comparison of their performance in terms of various accuracy and computation time measurements. The simulation results demonstrate that the hybrid GCM has higher accuracy and convergence than the remaining two GCMs in all cases. By directly comparing the primitive variables along the boundary, it can be concluded that the hybrid GCM has significant advantages in compressible flow simulations. The results of CPU time show that the hybrid GCM can provide more accurate results while ensuring the efficiency of the calculation.

A strong coupling prediction-correction immersed boundary method

In the traditional immersed boundary methods for solving compressible fluid-structure interaction problems, conservation is one of the problems that must be considered. When the coupling boundary moves on the fixed grid, the structure coverage will change, resulting in many dead elements and emerging elements on the fluid grid. In the ghost-cell immersed boundary method, the reconstructed grid can not maintain the strict mass conservation when the dead elements and emerging elements appear. In order to overcome the shortcomings of traditional methods, a strong coupling prediction-correction immersed boundary method for compressible fluid-structure interaction problems was proposed. Firstly, the matrix representation of a general fluid-structure coupling system was described, and a strong coupling Gauss-Seidel iterative scheme of fluid-structure coupling system was derived. Furthermore, a prediction-correction scheme was derived, and a prediction-correction immersed boundary method was proposed. The fluid-structure coupling boundary was regarded as a free surface, and the space originally occupied by the solid was initialized as zero mass elements, allowing the fluid to pass through the coupling boundary freely. For the calculation of fluid, the second-order MUSCL finite volume scheme with the minmod limiter and the AUSM+-up flux based on Zha-Bilgen splitting were used to advance the time step with the third-order Runge-Kutta scheme. In the correction step, the transport process was realized by a set of mass conservation transport rules. The transport algorithm could be summarized as marking the fluid inside the boundary, dividing and moving the fluid in a uniform way according to the marking order, generating a flow pointing to the outside of the boundary, and finally applying a velocity correction near the boundary to ensure the no-slip condition. The marking and transport algorithm avoided the tedious geometric treatment of the cut-cells, and ensured the easy implementation of the algorithm. For the calculation of solids, the first-order difference scheme and the implicit dynamic finite element scheme were used to solve the rigid body and linear elastic body respectively, and the Gauss quadrature was used to obtain the coupling force on the solid surface. The one-dimensional and two-dimensional problems were calculated by the prediction-correction immersed boundary method. In the one-dimensional piston problem, the accuracy, conservation and convergence of the method were investigated by comparing the results with those in the literature. In the two-dimensional shock wave impact problem, the experimental optical schlieren images were compared with those obtained by the numerical simulation, and the deflection history of the plate structure was investigated. The study shows that this method can accurately maintain the mass conservation of the flow field and has the advantage of easy implementation, which is different from the traditional ghost-cell method and the cut-cell method. This method has the first-order convergence accuracy, and can accurately predict the flow field after shock diffraction and the deflection of plate under shock waves. It provides a new idea for the development of fluid-structure coupling algorithms.

A ghost-cell immersed boundary method on preventing spurious oscillations for incompressible flows with a momentum interpolation method

We propose a ghost-cell immersed boundary method (GCIBM) using a local directional ghost cell approach for the simulation of incompressible flows involving solid geometry. The proposed method is based on a finite volume solver with a momentum interpolation method (MIM) on a collocated grid for the Navier-Stokes equations that is spatially discretized by a fourth-order compact scheme and temporally advanced by a fourth-order Runge-Kutta scheme. A new stencil for imposing the Neumann boundary is constructed following the least square regression. The spurious oscillations that spread from the immersed boundary are observed when the discrete momentum forcing (DMF) is obtained at the cell centers for velocities. This is due to the decoupling of the pressure and velocity fields. In this paper, the spurious oscillations are removed by the recovery of the decoupling by shifting the locations of DMF from the cell centers to the face centers. The efficiency of the proposed technique is confirmed in terms of a simulation for steady and unsteady flows with a stationary or moving geometry.

A ghost-cell immersed boundary method for unified simulations of flow over finite- and zero-thickness moving bodies at large CFL numbers

A ghost-cell immersed boundary method for unified simulations of flow over finite- and zero-thickness moving bodies at large Courant-Friedrichs-Lewy (CFL) numbers is presented. In order to handle such bodies in a unified manner, algorithms for interface construction and cell demarcation are proposed. The main challenge in treating zero-thickness bodies is to maintain sharpness and accuracy even at large CFL numbers with diminished spurious force oscillations. Thus, the effect of large CFL numbers on the solution accuracy of fluid-structure interaction (FSI) problems involving zero-thickness bodies is investigated and necessary treatments to preserve solution accuracy even at large CFL numbers are suggested. The present study suggests two treatments which are important in preserving the accuracy and stability of the solution: backward time integration for computational cells called ‘swept-cells’ and pressure boundary condition with mass conservation. Composite implicit time integration for the dynamic equation of a thin elastic structure is employed for a stable simulation of FSI at large CFL numbers. By using large time step sizes, the present method not only enhances computational efficiency, but also suppresses spurious force oscillations while maintaining the sharpness of an infinitesimally thin body. The efficacy and accuracy of the present method are examined through numerical examples.

A Ghost-Cell Immersed Boundary Method for Wave–Structure Interaction Using a Two-Phase Flow Model

The air-water two-phase flow model is developed to study the transformation of monochromatic waves passing over the submerged structure. The level set method is employed to describe the motion of the interface while the effect of the immersed object on the fluid is resolved using the ghost-cell immersed boundary method. The computational domain integrated with the air-water and fluid-solid phases allows the use of uniform Cartesian grids. The model simulates the wave generation, wave decomposition over a submerged trapezoidal breakwater, and the formation of the vortices as well as the drag and lift forces caused by the surface waves over three different configurations of the submerged structures. The numerical results show the capability of the present model to accurately track the deformation of the free surface. In addition, the variation of the drag and lift forces depend on the wavelength and wave induced vortices around the submerged object. Hence, the study observes that the triangular structure experiences the relatively small wave force.

Numerical simulation of water entry of two-dimensional structures with complex geometry using a CIP-based model

The present study extends the CIP-based model for the treatment of water entry of two-dimensional structures with complex geometry. The high-order difference model, where the modified ghost-cell immersed boundary method is taken to deal with the moving body with complex geometry more accurately, and the convection term is discretized by the CIP (Constrained Interpolation Profile) method and the free surface is captured by the THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method. The benchmarks are the symmetric water entry of a two-dimensional ship section in single degree of freedom and asymmetric water entry of a two-dimensional bionic dolphin section in three degrees of freedom. The impact peaks of local pressure and local force can be accurately predicted. The phenomena of the secondary impact and the air entrapment can be reproduced with fairly good accuracy. A further observation is that diving two-dimensional bionic dolphin section can use the horizontal velocity to increase the maximum penetration depth while maintaining relative stability in the engineering applications. These numerical investigations can help us to understand the influence of complex geometric parameters on hydrodynamic behavior.

High-Order WENO Schemes with an Immersed Boundary Method for Shallow Water Equations on the Tsunami Mitigation with Configurations of Cylinder Array

In this paper, we investigated the flow around vertical circular cylinders with the numerical simulation of shallow water equations. Since tsunami tidal waves have large potential energy due to height difference, the man-made structures near coast are heavily damaged during the propagation of waves. For the damage mitigation of natural disaster, a careful configuration of such obstructive structures is worthy of attention, and it is of great practical importance to provide numerical simulation based on the ideal models of natural or artificial structures in a coastal area. The simplified numerical models are listed as the single large cylinder and four small cylinders of double inline, double staggered, and single four arrangement with fixing the same blockage ratio. Among various up-to-date schemes, the fifth-order WENO scheme is selected with a ghost-cell immersed boundary method, which enabled the easy detection of the arbitrary body shapes emerged in background Cartesian grids. In addition, we proposed the non-reflecting characteristic boundary condition based on the characteristic compatibility equations derived in shallow water equations to suppress the unexpected reflection waves at the open boundary. The analysis on a benchmark problem on solitary wave reflection led to an expected validation with the present numerical model. Finally, reflection and diffraction of a tsunami wave are analyzed against a single and four cylinders of the same blockage density, and it is believed to reduce 20.80% points for the best case of single four cylinders in the view of dissipation ratio defined by the kinematic power.

A ghost-cell discrete unified gas kinetic scheme for thermal flows with heat flux at curved interface

The discrete unified gas kinetic scheme (DUGKS) is advanced for simulating thermal convections with curved heat flux condition using the ghost-cell (GC) approach. The fluid flow and temperature field combined under the Boussinesq approximation are solved by the double-population model. The ghost-cell immersed boundary method is applied to the curved heat-flux interface, where fictitious cells are set in the solid domain. The information at the centers of those cells is extrapolated from the fluid-solid interface and the neighboring flow. The heat-flux boundary condition at the interface can then be incorporated into the solution of the entire thermal flow. Note that the extrapolation/interpolation involved in the GC-DUGKS is accomplished through a sharp interface manner. Therefore, the difficulty in handling the heat-flux boundary condition for the diffuse-type immersed boundary methods due to the cross contamination is removed. Furthermore, the thermal buoyancy force is conveniently combined with the governing equation by the Strang-splitting scheme. Simulations of several well-established convection-diffusion flow problems with heat flux at the curved interface are performed to validate the present GC-DUGKS. The results demonstrate the accuracy and feasibility of the method.

A Radial Basis Function–Based Ghost Cell Method for Complex Rigid or Flexible Moving Boundary Flows

A radial basis function (RBF)-based ghost cell method is presented to simulate flows around a rigid or flexible moving hydrofoil on a Cartesian grid. A compactly supported radial basis function (CSRBF) is introduced to the ghost cell immersed boundary method to treat the complex flexible boundaries in the fluid. The results indicate that this RBF representation method can accurately track tempo-spatially varied interfaces and avoid the identification failure encountered in original RBF. In addition, an interface cell interpolation method is developed to treat the irregular boundaries such as sharp points and thin boundaries. Solution quality is improved by constructing the interface cells along the local irregular boundaries, instead of the ghost cells. To validate the proposed method, uniform flows around stationary and pitching hydrofoils are simulated. Then, a flexible hydrofoil undulating in the fluid is simulated. Good agreements are obtained by comparing the present results with the reference results. Furthermore, the relationship between the oscillation frequency and the force coefficient is studied. Also, generation mechanism of the thrust force is explained.

Fully resolved simulation of a shockwave interacting with randomly clustered particles via a ghost-cell immersed boundary method

Fully resolved direct numerical simulations are performed to investigate the interaction between a planar shockwave and 300 randomly clustered particles. The particle interfaces are captured with the ghost-cell immersed boundary method. Four cases of different shock Mach numbers up to 6.0 are investigated with a relatively high volume fraction of 14.7% of clustered particles. Results show that the reflected shocks form a planar shockwave propagating upstream, with its velocity decreasing with the increase in Mach number. In small Mach number cases, the transmitted shock remains planar and exceeds its original propagating speed. In high Mach number cases, the transmitted shock is highly curved and slowed down. The peak drag coefficients of all particles could exhibit a linear correlation with the streamwise location. The lift force coefficients could become similar to or even larger than the drag coefficients when the particles reside in post-shock regions. The peak lift force coefficients are the smallest for the first and last rows, and highest in the first half part of clusters, which is due to different mechanisms. The transverse effects of shock–cluster interaction are stronger in higher Mach number cases. This result indicates that the transverse force could not be ignored in a particle cluster with a relatively high volume fraction, especially when the Mach number is high. Fluctuating flow quantities indicate that the increase in Mach number could enhance the fluctuations in the transverse direction and reduce the streamwise mean velocity, resulting in stronger fluctuating fields compared with the mean flows.

Drag force for a burning particle

Fully-resolved simulations of a burning char particle are performed to understand the effects of chemical reactions on the drag force by using the ghost cell immersed boundary method. The momentum, heat and mass transfers at the interface are all considered. Reactive particle with different reaction rates, temperatures and diameters are simulated and compared with a non-reactive adiabatic particle and a particle with an outflow. The results show that both the heterogeneous reactions and the gaseous reactions increase the drag force, which is converse to the effect observed for a non-reactive particle with a pure outflow. This difference indicates that the species and temperature distributions caused by the chemical reactions around the particle play an important role in shaping the drag force. To consider these effects, the Stefan flow Reynolds number and the non-dimensional gaseous reaction rate are introduced to formulate a new drag force correlation for a burning particle based on the fully-resolved simulations. Good performance of the correlation has been demonstrated in the current conditions, and more evaluation might be required for future work.