Incompressible Flow Solver Research Articles

Implementation of density-based solver for all speeds in the framework of OpenFOAM

In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient. Program summaryProgram title: allSpeedUnsteadFoam/allSpeedUnsteadFoam_dualtimeCatalogue identifier: AETK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 255467No. of bytes in distributed program, including test data, etc.: 971156Distribution format: tar.gzProgramming language: C++.Computer: All capable of running Linux.Operating system: Linux.Has the code been vectorized or parallelized?: Yes ParallelizedRAM: 500 MB or moreClassification: 12.External routines: OpenFOAM (http://www.openfoam.org)Nature of problem:This software provides a library of models for the simulation of steady and unsteady all speeds flow field (all Mach number flow field including incompressible and compressible flow). Combining this library with other libraries within OpenFOAM, such as turbulence, radiation, solid conduction, etc., the more complex multi-physics model including all speeds flow field could be established conveniently.Solution method:Standard finite volume method (FVM) is used for solving all the preconditioned conservation governing equations. The preconditioned all speeds AUSM+(P) scheme is adopted to discretize the convective term in the governing equations. The total variation diminishing (TVD) scheme with interface reconstruction is used to improve the accuracy of this solver. The dual time scheme is used to solve the unsteady problem.Restrictions:The limiter functions have obvious effect on the accuracy of the numerical result and according to actual situation, so the selection of limiter functions should be focused on.Running time:It can vary from minutes to days to weeks depending on the size of the system, length of time simulated and number of processors used.

Numerical Investigation of Flow Control Feasibility with a Trailing Edge Flap

This paper concerns a numerical study of employing an adaptive trailing edge flap to control the lift of an airfoil subject to unsteady inflow conditions. The periodically varying inflow is generated by two oscillating airfoils, which are located upstream of the controlled airfoil. To establish the control system, a standard PID controller is implemented in a finite volume based incompressible flow solver. An immersed boundary method is applied to treat the problem of simulating a deformable airfoil trailing edge. The flow field is solved using a 2D Reynolds averaged Navier-Stokes finite volume solver. In order to more accurately simulate wall bounded flows around the immersed boundary, a modified boundary condition is introduced in the k- ω turbulence model. As an example, turbulent flow over a NACA 64418 airfoil with a deformable trailing edge is investigated. Results from numerical simulations are convincing and may give some highlights for practical implementations of trailing edge flap to a wind turbine rotor blade

A high‐order compact finite‐difference lattice Boltzmann method for simulation of steady and unsteady incompressible flows

SUMMARYA high‐order compact finite‐difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth‐order compact FD scheme, and the temporal term is discretized with the fourth‐order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high‐order spectral‐type low‐pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also conducted to evaluate the effects of grid size, filtering, and procedure of boundary conditions implementation on accuracy and convergence rate of the solution. The accuracy and efficiency of the proposed solution procedure based on the CFDLBM method are also examined by comparison with the classical LBM for different flow conditions. Two test cases considered herein for validating the results of the incompressible steady flows are a two‐dimensional (2‐D) backward‐facing step and a 2‐D cavity at different Reynolds numbers. Results of these steady solutions computed by the CFDLBM are thoroughly compared with those of a compact FD Navier–Stokes flow solver. Three other test cases, namely, a 2‐D Couette flow, the Taylor's vortex problem, and the doubly periodic shear layers, are simulated to investigate the accuracy of the proposed scheme in solving unsteady incompressible flows. Results obtained for these test cases are in good agreement with the analytical solutions and also with the available numerical and experimental results. The study shows that the present solution methodology is robust, efficient, and accurate for solving steady and unsteady incompressible flow problems even at high Reynolds numbers. Copyright © 2014 John Wiley & Sons, Ltd.

An overset grid method for integration of fully 3D fluid dynamics and geophysics fluid dynamics models to simulate multiphysics coastal ocean flows

It is now becoming important to develop our capabilities to simulate coastal ocean flows involved with distinct physical phenomena occurring at a vast range of spatial and temporal scales. This paper presents a hybrid modeling system for such simulation. The system consists of a fully three dimensional (3D) fluid dynamics model and a geophysical fluid dynamics model, which couple with each other in two-way and march in time simultaneously. Particularly, in the hybrid system, the solver for incompressible flow on overset meshes (SIFOM) resolves fully 3D small-scale local flow phenomena, while the unstructured grid finite volume coastal ocean model (FVCOM) captures large-scale background flows. The integration of the two models are realized via domain decomposition implemented with an overset grid method. Numerical experiments on performance of the system in resolving flow patterns and solution convergence rate show that the SIFOM-FVCOM system works as intended, and its solutions compare reasonably with data obtained with measurements and other computational approaches. Its unparalleled capabilities to predict multiphysics and multiscale phenomena with high-fidelity are demonstrated by three typical applications that are beyond the reach of other currently existing models. It is anticipated that the SIFOM-FVCOM system will serve as a new platform to study many emerging coastal ocean problems.

Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates

In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar–Gross–Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the implementation of the high-order compact finite-difference Lattice Boltzmann method (CFDLBM) in the generalized curvilinear coordinates is robust, efficient and accurate for solving steady and unsteady incompressible flows over practical geometries.

A matrix-form GSM–CFD solver for incompressible fluids and its application to hemodynamics

A GSM---CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM---CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper.

IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems

The Incompressible Flow & Iterative Solver Software (\ifiss) package contains software which can be run with MATLAB or Octave to create a computational laboratory for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions, together with state-of-the-art preconditioned iterative solvers for the resulting discrete linear equation systems. In this paper we give a flavor of the code's main features and illustrate its applicability using several case studies. We aim to show that \ifiss can be a valuable tool in both teaching and research.

Numerical solution of the two-phase incompressible Navier–Stokes equations using a GPU-accelerated meshless method

Abstract This paper presents the development and implementation of a Meshless two-phase incompressible fluid flow solver and its acceleration using the graphics processing unit (GPU). The solver is formulated as a Localized Radial-Basis Function Collocation Meshless Method and the interface of the two-phase flow is captured using an implementation of the Level-Set method. The Compute Unified Device Architecture (CUDA) language for general-purpose computing on the GPU is used to accelerate the solver. Through the combined use of the LRC Meshless method and GPU acceleration this paper seeks to address the issue of robustness and speed in computational fluid dynamics. Traditional mesh-based methods require extensive and time-consuming user input for the generation and verification of a computational mesh. The LRC meshless method seeks to mitigate this issue through the use of a set of scattered points that need not meet stringent geometric requirements like those required by finite-volume and finite-element methods, such as connectivity and poligonalization. The method is shown to render very accurate and stable solutions and the implementation of the solver on the GPU is shown to accelerate the solution by several orders.

A Pressure-Based Segregated Solver for Incompressible Flow on Unstructured Grids

In this article, a novel finite-volume solver for the two-dimensional incompressible flow on unstructured grids is presented. The solver is formulated to operate on any type of control volumes. The performance of the new algorithm as compared to the SIMPLE algorithm is tested by solving three benchmark problems using both methodologies and comparing their computational costs. Results indicate that the new algorithm can reach convergence in a more wide parameter range and it is at least two times faster than the SIMPLE algorithm. The advantage of the new algorithm is especially evident for the case of high Reynolds number.

A general purpose parallel block structured open source incompressible flow solver

A general purpose incompressible flow solver, called caffa3d.MBRi, is presented which features a block structured framework to accommodate both a flexible approach to geometry representation and a straightforward implementation of parallel capabilities through the MPI library. Representation of complex geometries can be handled semi automatically through a combination of body fitted blocks of grids and the immersed boundary condition strategy over both Cartesian and body fitted grid blocks. The parallelization strategy is based on the same block structured framework, by means of encapsulated MPI calls performing a set of conceptually defined high level communication tasks. A set of real world applications ranging from bioengineering to microclimate scenarios is presented to demonstrate the capabilities of the solver, which is open source and freely available through the web page.

A Hermite pseudospectral solver for two-dimensional incompressible flows on infinite domains

The Hermite pseudospectral method is applied to solve the Navier–Stokes equations on a two-dimensional infinite domain. The feature of Hermite function allows us to adopt larger time steps than other spectral methods, but also leads to some extra computation when the stream function is calculated from the vorticity field. The scaling factor is employed to increase the resolution within the region of our main interest, and the aliasing error is fully removed by the 2/3-rule. Several traditional numerical experiments are performed with high accuracy, and some related future work on physical applications of this program is also discussed.

Numerical investigation of a jet and vortex actuator in a cross flow boundary layer

The performance of a zero-net-mass-flux Jet and Vortex Actuator (JaVA) was numerically investigated in a two-dimensional-cross-flow flat-plate laminar boundary layer. The JaVA is an active flow control device that can be used for flow separation control and thus can delay/prevent boundary layer separation. In this study, an unsteady, incompressible flow solver has been used to study the flow fields generated by a JaVA in a water channel. Detailed quantitative information about the performance of the JaVA on a flat-plate boundary layer is obtained. JaVA-induced boundary-layer profiles are clearly ‘fuller’ at the wall and hence more resistant to flow separation. The ‘positive’ effects of the JaVA with different operating regimes on various boundary-layer flow characteristics such as displacement thickness, shape factor and the friction coefficient are presented in this study. Selecting the appropriate governing parameters in conjunction with cross-flow properties, the velocity profile can be tuned in a boundary layer to delay or prevent separation.

Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems

Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

A three-dimensional numerical model for dense granular flows based on the [formula omitted] rheology

This paper presents a three-dimensional implementation of the so-called μ(I) rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton–Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data.

입구 및 출구 형상 변화에 따른 촉매 삽입형 머플러 내부의 유동 해석

Lack of the space in many diesel vehicles make it difficult to design and install the catalytic muffler to reduce emissions. For this reason, inlet part of the catalytic muffler is made of L-type which has lower flow uniformity than conventional I-type, and catalytic muffler has complex internal structure by various insertions, which affect the flow uniformity and pressure drop of the systems. In this work, the flow characteristics such as flow uniformity and pressure drop have been numerically investigated by changing such various geometries as inlet shape, porosity, and outlet shape inside the muffler with the three-dimensional turbulent incompressible flow solver. Total 4 different cases are considered in order to find optimal configurations of the catalytic muffler in view of high flow uniformity and low pressure drop. The results show that Case 2 which has no induction cone and outlet perforated pipe has higher uniformity index and lower pressure drop than others considered in this work.

A novel multiblock immersed boundary method for large eddy simulation of complex arterial hemodynamics

Computational fluid dynamics (CFD) simulations are becoming a reliable tool to understand hemodynamics, disease progression in pathological blood vessels and to predict medical device performance. Immersed boundary method (IBM) emerged as an attractive methodology because of its ability to efficiently handle complex moving and rotating geometries on structured grids. However, its application to study blood flow in complex, branching, patient-specific anatomies is scarce. This is because of the dominance of grid nodes in the exterior of the fluid domain over the useful grid nodes in the interior, rendering an inevitable memory and computational overhead. In order to alleviate this problem, we propose a novel multiblock based IBM that preserves the simplicity and effectiveness of the IBM on structured Cartesian meshes and enables handling of complex, anatomical geometries at a reduced memory overhead by minimizing the grid nodes in the exterior of the fluid domain. As pathological and medical device hemodynamics often involve complex, unsteady transitional or turbulent flow fields, a scale resolving turbulence model such as large eddy simulation (LES) is used in the present work. The proposed solver (here after referred as WenoHemo), is developed by enhancing an existing in-house high-order incompressible flow solver that was previously validated for its numerics and several LES models by Shetty et al. (2010) [33]. In the present work, WenoHemo is systematically validated for additional numerics introduced, such as IBM and the multiblock approach, by simulating laminar flow over a sphere and laminar flow over a backward facing step respectively. Then, we validate the entire solver methodology by simulating laminar and transitional flow in abdominal aortic aneurysm (AAA). Finally, we perform blood flow simulations in the challenging clinically relevant thoracic aortic aneurysm (TAA), to gain insights into the type of fluid flow patterns that exist in pathological blood vessels. Results obtained from the TAA simulations reveal complex vortical and unsteady flow fields that need to be considered in designing and implanting medical devices such as stent grafts.

OpenFOAM의 비압축성 유동 해석정밀도 평가

The goal of the research is to evaluate the open source code of OpenFOAM for the use of nuclear plant flow simulation objectively. Of the various incompressible flow solvers, simpleFoam, pimpelFoam are then tested under three validated cases (backward facing step, flow over circular cylinder and turbulent round jet flow). For the evaluation of steady state incompressible laminar flow simulation, low reynolds number of backward facing step flow was solved by simpleFoam. The resultant of the reattached lengths turned out to be similar with the other experimental and simulation results. For transient flow simulation, flow over circular cylinder and turbulent round jet flow were solved by pimpleFoam. The simulation accuracy was evaluated by comparing the resultant flow patterns with the description of the characteristics of the flow over the circular cylinder. The quantitative accuracy was evaluated for no more than 85% by comparing it to the decaying constants of the turbulent round jet velocity.

Large scale simulation of red blood cell aggregation in shear flows

Aggregation of highly deformable red blood cells (RBCs) significantly affects the blood flow in the human circulatory system. To investigate the effect of deformation and aggregation of RBCs in blood flow, a mathematical model has been established by coupling the interaction between the fluid and the deformable solids. The model includes a three-dimensional finite volume method solver for incompressible viscous flows, the combined finite-discrete element method for computing the deformation of the RBCs, a JKR model–Johnson, Kendall and Roberts (1964–1971) (Johnson et al., 1971) to take account of the adhesion forces between different RBCs and an iterative direct-forcing immersed boundary method to couple the fluid–solid interactions. The flow of 49,512 RBCs at 45% concentration under the influence of aggregating forces was examined, improving the existing knowledge on simulating flow and structural characteristics of blood at a large scale: previous studies on the particular issue were restricted to simulating the flow of 13,000 aggregative ellipsoidal particles at a 10% concentration. The results are in excellent agreement with experimental studies. More specifically, both the experimental and the simulation results show uniform RBC distributions under high shear rates (60–100/s) whereas large aggregation structures were observed under a lower shear rate of 10/s. The statistical analysis of the simulation data also shows that the shear rate has significant influence on both the flow velocity profiles and the frequency distribution of the RBC orientation angles.

Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers

Synthetic turbulence for inflow conditions formulated on a 2-D plane generally produces unphysically large pressure fluctuations in direct numerical and large-eddy simulations. To reduce such artificial fluctuations a divergence-free method is developed with incompressible flow solvers. The procedure of the velocity–pressure solvers is slightly modified on a vertical plane near (rather than at) the inlet by inserting the synthetic turbulence on that plane during the procedure. Simple analytic and numerical error estimations are used to show that the impact of the modified solvers on solution accuracy is small. The final synthetic turbulence satisfies the divergence-free condition. No additional CPU time is required to achieve this condition. The method was tested via simulations of a plane channel flow with Reτ=395. Reynolds stresses, wall skin friction and power spectra of velocity fluctuations are compared with those obtained from using periodic inlet–outlet boundary conditions. In particular, the variances and power spectra of pressure fluctuations are shown to be accurately predicted only when the divergence-free inlet condition is used.

Implementation of all‐Mach Roe‐type schemes in fully implicit CFD solvers – demonstration for wind turbine flows

SUMMARYThis paper presents the implementation of all‐Mach Roe‐type schemes in a fully implicit CFD solver. Simple 2D cases, such as the flow around inviscid and viscous aerofoils, were used for an initial validation of these methods, along with more challenging computations consisting of the 3D flow around the Model Experiments in Controlled Conditions wind turbine, in parked and rotating conditions. This work is motivated by the increased interest of the wind turbine industry in larger diameter wind turbines where compressibility effects near the blade tips may be important. Instead of using an incompressible flow solver, this paper explores the option of modifying an existing, efficient, compressible flow solver for use at lower Mach numbers. The good performance of the Roe solver and its popularity influenced the selection of schemes for this work. The results suggest that effective all‐Mach solutions are possible with implicit solvers, and the paper defines the implementation of the new fluxes and Jacobian, including an investigation of some numerical parameters, using as platform the Helicopter Multi‐Block solver of Liverpool University. Copyright © 2013 John Wiley & Sons, Ltd.