Cut Cell Mesh Research Articles

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Validation of CFD model for simulation of multi-pipe earth-to-air heat exchangers (EAHEs) flow performance

In this paper the experimentally obtained flow characteristics of multi-pipe earth-to-air heat exchangers (EAHEs) were used to validate the EAHE flow performance numerical model prepared by means of CFD software Ansys Fluent. The cut-cell meshing and the k-ε realizable turbulence model with default coefficients values and enhanced wall treatment were used. The total pressure losses and airflow in each pipe of multi-pipe exchangers was investigated both experimentally and numerically. The results show that airflow in each pipe of the multi-pipe EAHE structures is not equal. The validated numerical model can be used for a proper designing of multi-pipe EAHEs from the point of view of the flow characteristics. The influence of EAHEs geometrical parameters on the total pressure losses and airflow division between the exchanger pipes can also be analyzed. Usage of CFD for a designing process of EAHEs can be helpful for HVAC engineers (Heating Ventilation and Air Conditioning). It can also be helpful for optimizing the geometrical structure of multi-pipe EAHEs in order to save the energy and decrease operational costs of low-energy buildings.

Analysis of Near-wall effect on cloud cavitating flow that surrounds an axisymmetric projectile using large eddy simulation with Cartesian cut-cell mesh method

Near-wall effect is important for cavitation of flow and vortex structures. These structures are commonly investigated in cavitation of tip-vortex leakage, but are rarely discussed in cloud cavitating flow. In this study, typical experiments and numerical simulation of cloud cavitating flow were conducted near a wall that surrounds an underwater axisymmetric projectile. The experimental observations of cavity development are consistent with numerical results and validate the method’s accuracy. Changes in the cavity of the distal and near wall side differ throughout the entire evolution process. The cavity grows faster on the near wall side than on the distal side, whereas the re-entry jet inside the cavity moves slowly toward the shoulder of the model. The strong vortex around the projectile is non-axisymmetric because of the collapsing cavity, which may also affect the cruising stability.

Cloud Cavitating Flow That Surrounds a Vertical Hydrofoil Near the Free Surface

Unstable cavitation presents an important speed barrier for underwater vehicles such as hydrofoil craft. In this paper, the authors concern about the physical problem about the cloud cavitating flow that surrounds an underwater-launched hydrofoil near the free surface at relatively high-Froude number, which has not been discussed in the previous research. A water tank experiment and computational fluid dynamics (CFD) simulation are conducted in this paper. The results agree well with each other. The cavity evolution process in the experiment involves three stages, namely, cavity growth, shedding, and collapse. Numerical methods adopt large eddy simulation (LES) with Cartesian cut-cell mesh. Given that the speed of the model changes during the experiment, this paper examines cases with varying constant speeds. The free surface effects on the cavity, re-entry jet location, and vortex structures are analyzed based on the numerical results.

Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes

Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidimensional transport schemes avoid splitting errors on distorted, arbitrary meshes, and method-of-lines schemes have a low computational cost because they perform reconstructions at fixed points.This paper presents a multidimensional method-of-lines finite volume transport scheme, “cubicFit”, which is designed to be numerically stable on arbitrary meshes. Stability conditions derived from a von Neumann stability analysis are imposed during model initialisation to obtain stability and improve accuracy in distorted regions of the mesh, and near steeply-sloping lower boundaries. Reconstruction calculations depend upon the mesh only, needing just one vector multiply per face per time-stage irrespective of the velocity field.The cubicFit scheme is evaluated using three, idealised numerical tests. The first is a variant of a standard horizontal transport test on severely distorted terrain-following meshes. The second is a new test case that assesses accuracy near the ground by transporting a tracer at the lower boundary over steep terrain on terrain-following meshes, cut-cell meshes, and new, slanted-cell meshes that do not suffer from severe time-step constraints associated with cut cells. The third, standard test deforms a tracer in a vortical flow on hexagonal–icosahedral meshes and cubed-sphere meshes. In all tests, cubicFit is stable and largely insensitive to mesh distortions, and cubicFit results are more accurate than those obtained using a multidimensional linear upwind transport scheme. The cubicFit scheme is second-order convergent regardless of mesh distortions.

Numerical study of periodic long wave run-up on a rigid vegetation sloping beach

Coastal vegetation can reduce long wave run-up on beaches and inland propagation distances and thus mitigate these hazards. This paper investigates periodic long wave run-up on coastal rigid vegetation sloping beaches via a numerical study. Rigid vegetation is approximated as rigid sticks, and the numerical model is based on an implementation of Morison's formulation [21] for rigid structures induced inertia and drag stresses in the nonlinear shallow water equations. The numerical model is solved via a finite volume method on a Cartesian cut cell mesh. The accuracy of the numerical model is validated by comparison with experimental results. The model is then applied to simulate various hypothetical cases of long periodic wave run-up on a sloping vegetated beach with different plant diameters and densities, and incident long waves with different periods. The sensitivity of long wave run-up to plant diameter, stem density and wave period is investigated by comparison of the numerical results for different vegetation characteristics and different wave periods. The numerical results show that rigid vegetation can effectively reduce long wave run-up and that wave run-up is decreased with increase of plant diameter and stem density. Moreover, the attenuation of long periodic wave run-up due to vegetation is sensitive to the variation of the incident wave period, and the attenuation of wave run-up is not increased or decreased monotonically with incident wave period.

Experimental investigation and CFD simulation of multi-pipe earth-to-air heat exchangers (EAHEs) flow performance

In this paper the experimentally obtained flow characteristics of multi-pipe earth-to-air heat exchangers (EAHEs) were used to validate the EAHE flow performance numerical model prepared by means of CFD software Ansys Fluent. The cut-cell meshing and the k-ε realizable turbulence model with default coefficients values and enhanced wall treatment was used. The total pressure losses and airflow in each pipe of multi-pipe exchangers was investigated both experimentally and numerically. The results show that airflow in each pipe of multi-pipe EAHE structures is not equal. The validated numerical model can be used for a proper designing of multi-pipe EAHEs from the flow characteristics point of view. The influence of EAHEs geometrical parameters on the total pressure losses and airflow division between the exchanger pipes can be also analysed. Usage of CFD for designing the EAHEs can be helpful for HVAC engineers (Heating Ventilation and Air Conditioning) for optimizing the geometrical structure of multi-pipe EAHEs in order to save the energy and decrease operational costs of low-energy buildings.

An Explicit Implicit Scheme for Cut Cells in Embedded Boundary Meshes

We present a new mixed explicit implicit time stepping scheme for solving the linear advection equation on a Cartesian cut cell mesh. We use a standard second-order explicit scheme on Cartesian cells away from the embedded boundary. On cut cells, we use an implicit scheme for stability. This approach overcomes the small cell problem--that standard schemes are not stable on the arbitrarily small cut cells--while keeping the cost fairly low. We examine several approaches for coupling the schemes in one dimension. For one of them, which we refer to as flux bounding, we can show a TVD result for using a first-order implicit scheme. We also describe a mixed scheme using a second-order implicit scheme and combine both mixed schemes by an FCT approach to retain monotonicity. In the second part of this paper, extensions of the second-order mixed scheme to two and three dimensions are discussed and the corresponding numerical results are presented. These indicate that this mixed scheme is second-order accurate in $$L^1$$L1 and between first- and second-order accurate along the embedded boundary in two and three dimensions.

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

Further Application of Surface Capturing Method and Cartesian Cut Cell Mesh on Hydroelastic Water-Entry Problems of Free-Falling Elastic Wedge

In order to study the interactions between fluid and elastic structure (such as marine lifeboat falling down and ship), this paper presents a new CFD method on hydroelastic water-entry problem of free-falling elastic wedge, which can more conveniently handle moving solid boundaries. In the CFD solver, a surface capturing method and the Cartesian cut cell mesh are employed to deal with the moving free surface and solid boundaries, respectively. On the other hand, in structural analysis, the finite element method and lath-beam structural model are introduced to calculate the elastic response. Furthermore, based on the current CFD and structural solver, a particular data transfer method and coupling strategy are presented for the fluid-structure interaction. Finally, by comparing numerical results with experimental data, the present method is validated to be available and feasible for hydroelastic water-entry problem and further successfully adopted to analyze the motion characteristics of free-falling elastic wedge.

CFD-Based Calculation of Regular Transverse Wave Force in the Maneuvering Mathematical Modeling Group (MMG) Model

The accuracy of mathematical model has a great effect on the prediction of ships maneuverability. Wave disturbing force is an important element of the Maneuvering Mathematical Modeling Group (MMG). Building regression formula of wave disturbing force acting on the ship hull can not only increase ship mathematical models accuracy but also help to predict ships maneuverability. The wave force can be calculated by the Computational Fluid Dynamics (CFD) method, which is more accurate and economical. The 3D model of M/V YUKUN was established and the cut-cell mesh was made. A numerical wave tank was developed in this work, based on the FLUENT software. The calculation results were obtained with different height, length, and period of waves. After analyzing the calculated data obtained by the CFD simulation, a regression formula was built about the above parameters. Finally, after comparing the regression formula and tradition wave force model based on the slender body theory, it can be concluded that the regular transverse wave force regression formula of the YUKUN is valid and better to make simulation for the prediction on ships maneuverability.

Numerical study of vegetation damping effects on solitary wave run-up using the nonlinear shallow water equations

Vegetation damping effects on propagating water waves have been investigated by many researchers. This paper investigates the effects of damping due to vegetation on solitary water wave run-up via numerical simulation. The numerical model is based on an implementation of Morison's formulation for vegetation induced inertia and drag stresses in the nonlinear shallow water equations. The numerical model is solved via a finite volume method on a Cartesian cut cell mesh. The accuracy of the numerical scheme and the effects of the vegetation terms in the present model are validated by comparison with experiment results. The model is then applied to simulate a solitary wave propagating on a plane slope with vegetation. The sensitivity of solitary wave run-up to plant height, diameter and stem density is investigated by comparison of the numerical results for different patterns of vegetation. The numerical results show that vegetation can effectively reduce solitary wave propagation velocity and that solitary wave run-up is decreased with increase of plant height in water and also diameter and stem density.

Numerical Simulation of Water Impact on a Wave Energy Converter in Free Fall Motion

Results are presented for the 3D numerical simulation of the water impact of a wave energy converter in free fall and subsequent heave motion. The solver, AMAZON-3D, employs a Riemann-based finite volume method on a Cartesian cut cell mesh. The computational domain includes both air and water regions with the air/water boundary captured automatically as a discontinuity in the density field thereby admitting break up and recombination of the free surface. Temporal discretisation uses the artificial compressibility method and a dual time stepping strategy. Cartesian cut cells are used to provide a boundary-fitted grid at all times. The code is validated by experimental data including the free fall of a cone and free decay of a single Manchester Bobber component.

A Cartesian cut cell free surface capturing method for 3D water impact problems

SUMMARYA Cartesian cut cell mesh generation procedure is developed together with a finite volume Euler solver for a two‐fluid system with a free surface. A fast and robust triangle to triangle overlap scheme is used to determine the intersection of a body‐surface with the background Cartesian mesh. Improvements to the cut cell routines include a new treatment for multiple cuts within a single cell and a surface trimming procedure to ensure a good quality mesh around solid boundaries. The formulae for calculating all necessary information about a cut cell are also presented. These are generic and can be used for arbitrarily irregular boundary elements. A collocated finite volume method with a high resolution Godunov‐type scheme in space is used for discretization of the governing flow equations. By computing in both the air and water regions simultaneously in a consistent manner, the free surface is automatically captured as a contact discontinuity in the density field without the need for any special free surface tracking method. The algorithm incorporates the artificial compressibility method with a dual time stepping strategy to maintain a divergence free velocity field. The mathematical formulation including its numerical implementation of the method is reviewed and results for a number of test cases are also presented. Copyright © 2012 John Wiley & Sons, Ltd.

An Investigation of CutCell Meshing Strategies for Accurate Aerodynamic Performance Prediction

An Investigation of CutCell Meshing Strategies for Accurate Aerodynamic Performance Prediction

Analysis of Mechanical Energy Transport on Free‐Falling Wedge during Water‐Entry Phase

For better discussing and understanding the physical phenomena and body‐fluid interaction of water‐entry problem, here mechanical‐energy transport (wedge, fluid, and each other) of water‐entry model for free falling wedge is studied by numerical method based on free surface capturing method and Cartesian cut cell mesh. In this method, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method. Then artificial compressibility method, dual‐time stepping technique, and Roe′s approximate Riemann solver are applied in the numerical scheme. Furthermore, the projection method of momentum equations and exact Riemann solution are used to calculate the fluid pressure on solid boundary. On this basis, during water‐entry phase of the free‐falling wedge, macroscopic energy conversion of overall body‐fluid system and microscopic energy transformation in fluid field are analyzed and discussed. Finally, based on test cases, many useful conclusions about mechanical energy transport for water entry problem are made and presented.

Comments on ‘An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems’

In the paper entitled ‘An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems’ ( Wang & Wang 2009 Proc. R. Soc. A 465 , 1843–1868 ( doi:10.1098/rspa.2008.0410 )), the present authors' earlier work ( Qian et al . 2006 , Proc. R. Soc. A 462 , 21–42 ( doi:10.1098/rspa.2005.1528 )) has been specifically applied to the study of water-entry and -exit of solid objects. An extended boundary condition, retaining the term owing to acceleration of moving boundaries in the momentum equation, has been implemented for calculating the pressure gradient at solid surfaces and, based on their numerical experiments, it was concluded by Wang and Wang that without this term the calculation will substantially under-predict the impact forces and may even break down. Therefore, a more complex procedure based on the exact solution of a Riemann problem for moving boundaries was implemented. In this short comment, by applying the authors' free surface capturing code to the same flow problem of water-entry of a wedge, it can, however, be demonstrated that the results from implementing the new pressure boundary condition are nearly identical to that of employing the original boundary condition without the acceleration term, indicating that its effects on the simulation results are minimal. A further examination of the implementation details on the pressure boundary condition also supports this conclusion.

Numerical model for flood routing with a Cartesian cut-cell domain

Flood risk analysis requires adequate numerical modeling to estimate the inundation depth and velocity in a wide-ranging study area. Thus, accurate, simple, and efficient numerical models with adequate mesh systems are needed for large-scale flood simulations. A numerical model based on a finite volume approach with the Cartesian cut-cell method is adopted herein to solve the shallow-water equations. To improve the representation of the flow domain, a modified cut-cell technique is suggested. The modified cut-cell mesh can be generated by a mesh merging process which needs two or more cut-cell meshes for different flow characteristic domains such as a compound meandering channel with steps. The modified cut-cell mesh indicated a reasonable flow domain to represent complicated domains. To verify the accuracy and stability of the present numerical model, various tests were performed and the obtained predictions compared with available exact solutions and laboratory measurements. A very reasonable agreement was observed.

Space–time discontinuous Galerkin finite element method for two-fluid flows

A novel numerical method for two-fluid flow computations is presented, which combines the space–time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space–time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.

An essential solution of water entry problems and its engineering applications

For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh. In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method. Then artificial compressibility method, dual time-stepping technique and Roe’s approximate Riemann solver are adopted in the numerical scheme. Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.