Eulerian Finite Volume Method Research Articles

A Eulerian–Lagrangian Coupled Method for the Simulation of Submerged Granular Column Collapse

A two-fluid Eulerian–Lagrangian coupled model is developed to investigate the complex interactions between solid particles and the ambient water during the process of submerged granular column collapse. In this model, the water phase is considered to be a Newtonian fluid, whereas the granular column is modeled as an elastic–perfectly plastic material. The water flow field is calculated by the mesh-based Eulerian Finite Volume Method (FVM), with the free surface captured by the Volume-of-Fluid (VOF) technique. The large deformation of the granular material is simulated by the mesh-free, particle-based Lagrangian Smoothed Particle Hydrodynamics method (SPH). Information transfer between Eulerian nodes and Lagrangian particles is performed by the aid of the SPH interpolation function. Both dry and submerged granular column collapses are simulated with the proposed model. Experiments of the submerged cases are also conducted for comparison. Effects of dilatancy (compaction) of initially dense (loose) packing granular columns on the mixture dynamics are investigated to reveal the mechanisms of different flow regimes. Pore water pressure field and granular velocity field are in good agreement between our numerical results and experimental observations, which demonstrates the capability of the proposed Eulerian–Lagrangian coupled method in dealing with complex submerged water–granular mixture flows.

Numerical Simulation of Turbulent Blood Flow in the System of Coronary Arteries with Stenosis

In this paper, we propose a mathematical model of turbulence flow of fluid through a deformable channel to study the pulsatile blood flow in the coronary system with arterial stenosis. Blood is assumed to be an incompressible non- Newtonian fluid and its motion is considered as turbulent and modelled by the mass and momentum conservations with turbulent mixing energy and specific dissipation rate. The mechanical deformation of the arterial wall is modelled by a hyperelastic differential equation. The pulsatile behaviour during each heartbeat is assigned on the entrance and exit boundaries. Numerical simulation based on the Finite Element method for the solution of arterial wall deformation, and the Arbitrary Lagrangian Eulerian Finite Volume method for the turbulence fluid-flow solution is used to investigate the effect of stenosis severity at the proximal part of the left anterior descending artery on the blood velocity, the pressure distribution and the wall shear stresses along the flow direction.

A family of finite volume Eulerian–Lagrangian methods for two-dimensional conservation laws

We develop a family of finite volume Eulerian–Lagrangian methods for the solution of nonlinear conservation laws in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstructed using the modified method of characteristics, while an Eulerian method is used to discretize the conservation equation in a finite volume framework. The method is simple, accurate, conservative and it combines advantages of the modified method of characteristics to accurately solve the nonlinear conservation laws with an Eulerian finite volume method to discretize the equations. The proposed finite volume Eulerian–Lagrangian methods are conservative, non-oscillatory and suitable for hyperbolic or non-hyperbolic systems for which Riemann problems are difficult to solve or do not exist. Numerical results are presented for an advection–diffusion equation with known analytical solution. The performance of the methods is also analyzed on several applications in Burgers and Buckley–Leverett problems. The aim of such a method compared to the conventional finite volume methods is to solve nonlinear conservation laws efficiently and with an appropriate level of accuracy.

Projection finite volume method for shallow water flows

A simple and accurate projection finite volume method is developed for solving shallow water equations in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstructed using the method of characteristics, while an Eulerian method is used to discretize the conservation equations in a finite volume framework. The method is conservative and it combines advantages of the method of characteristics to accurately solve the shallow water flows with an Eulerian finite volume method to discretize the equations. Numerical results are presented for several applications in rotating shallow water problems. The aim of such a method compared to the conventional finite volume methods is to solve shallow water equations efficiently and with an appropriate level of accuracy.

Numerical Modeling of Advancing Wave Front in Dam Break Problem by Incompressible Navier-stokes Solver

A dam break resulting in the formation of bore waves and overflow of a dam downstream is simulated using an incompressible Navier-Stokes solver. Volume of Fluid (VOF) method is employed to capture the wave travel model which uses the Eulerian Finite Volume Method (FVM). General purpose computational fluid dynamics (CFD) code Fluent is used to perform the numerical computations. Free-surface elevation, velocity of flow etc. in the lower reservoir, before and subsequent variations after upstream dam collapse were monitored for nearly 10sec. Parametric study of the one dimensional wave impact on the dam downstream was found matching with the theoretical predictions which urges to consider greater problem complexities in future. Flow equations are developed considering the velocities in two dimensions. The behaviour of impacting wave front including the to and fro motion after collision; and damping is captured using VOF method. The relevance of time step size and grid size are discussed in detail. The parameters are non-dimensionalised for easier interpretation of the wave behaviour.

A higher‐order unsplit 2D direct Eulerian finite volume method for two‐material compressible flows based on the MOOD paradigms

SUMMARYA higher‐order unsplit multi‐dimensional discretization of the diffuse interface model for two‐material compressible flows proposed by R. Saurel, F. Petitpas and R. A. Berry in 2009 is developed. The proposed higher‐order method is based on the concepts of the Multidimensional Optimal Order Detection (MOOD) method introduced in three recent papers for single‐material flows. The first‐order unsplit multi‐dimensional Finite Volume discretization presented by SPB serves as foundation for the development of the higher‐order unlimited schemes. Specific detection criteria along with a novel decrementing algorithm for the MOOD method are designed in order to deal with the complexity of multi‐material flows. Numerically, we compare errors and computational times on several 1D problems (stringent shock tube and cavitation problems) computed on 2D meshes with the second‐ and fourth‐order MOOD methods using a classical MUSCL method as reference. Several simulations of a 2D shocked R22 bubble in the air are also presented on Cartesian and unstructured meshes with the second‐ and fourth‐order MOOD methods, and qualitative comparisons confirm the conclusions obtained with 1D problems. These numerical results demonstrate the robustness of the MOOD approach and the interest of using more than second‐order methods even for locally singular solutions of complex physics models. Copyright © 2014 John Wiley & Sons, Ltd.

Three-dimensional numerical and experimental investigation on friction stir welding processes of ferritic stainless steel

A three-dimensional thermomechanical simulation of friction stir welding (FSW) processes is carried out for ferritic stainless steel by utilizing an Eulerian finite volume method under the steady state condition, and the simulation result is compared directly with both the measured temperature histories during FSW and the microstructural changes after FSW. Based on a viscoplastic self-consistent approach for polycrystal, the texture development in the FSWed material is determined from the velocity gradients along the streamlines in the material flow field. The simulation results show that the heat is generated mainly near the interface between the tool and the workpiece, and that the viscosity changes drastically in the vicinity of the boundary between the stir zone and the thermomechanically affected zone. From the predicted streamlines, it can be indicated that the strong material flow mainly develops on the retreating side of the tool. Also, the simulation results show that the shear deformation texture is significantly developed in the FSWed region. The measured temperatures and microstructural characteristics agree fairly well with the predicted data.

The suction force effect analysis of large civil aircraft ditching

The research on ditching is indispensable for civil airplanes made in China to obtain the airworthiness certificates. The suction force effect in the ditching process is a hot and difficult research topic. In this paper, the explicit method is employed to solve the discrete Lagrangian finite element equations. The Eulerian finite volume method (FVM) is used to solve the Eulerian control equations; the fluid-solid coupling is realized through the general coupling method. The model of large civil airplane ditching is simulated by Dytran and the model test in tank is carried out in the same condition. Based on the analysis on the impacts and generation of the suction force and a numerical example, we obtain the accurate ditching pressure and pitch angle, as well as the results from the simulation and test. The estimated pressure and pitch angles are consistent with the results in the test. In the simulation, where the suction force is considered, the attitude-time history curve is very similar to the one of the tests, whereas the attitudes in the calculation without suction force is far different from the test. It can be concluded from the results that the suction force is the key impact in ditching calculation and can be simulated by general coupling method. In addition, different weight characteristics and different initial pitch angles both result in different pressures of ditching.

Numerical investigation of snow traction characteristics of 3-D patterned tire

Traction and braking performances of automobile tire on the snow road are quite distinct from those on the dry or wet road, because of the complicated snow deformation caused by the complex tread blocks. In fact, the mathematical formulation of the snow deformation is extremely difficult, because not only it depends on the loading condition but its material properties are significantly dependent on the icing state (i.e. the snow density). The purpose of the current study is to introduce a numerical simulation of the snow–tire interaction by making use of Lagrangian finite element method and Eulerian finite volume method. The interaction between the tire tread blocks and the snow deformation is implemented by the explicit Euler–Lagrangian coupling scheme. The multi-surface yield model is adopted to describe both the softening and yielding of snow, and the associated material properties are chosen based upon the existing data in literature and the preliminary verification simulation. The numerical experiments are carried out by MSC/Dytran to investigate the parametric characteristics of the snow traction to the snow hardness, the block depth and the tread pattern.

Research and Development of the Porthole-Die Aluminium Alloy Extrusion Processes

The current research on the porthole-die aluminium alloy extrusion is presented here. The empirical method and simulation method are analyzed. Particularly, the Lagrangian Finite Element Method(FEM), Eulerian Finite Volume Method(FVM) and Arbitrary-Lagrangian Eulerian(ALE) algorithm are compared. The development of the porthole-die aluminium is educed.

Analysis on the Hydroplaning of Aircraft Tire

Aircraft tire is an important subassembly of aircraft, which is related to its safety tightly, especially for civil aircraft. Moreover, hydroplaning of aircraft tires is often a contributing factor in take-off and landing overrun and veeroff accidents. Therefore the study on them is imperative. For studying the hydroplaning of aircraft tire, a 2D finite element model of aircraft tire is developed by using TYABAS software, and then a 3D patterned tire model is presented. The hydroplaning of aircraft tire is analyzed by generally coupling an Eulerian finite volume method and an explicit Lagrangian finite element method. The hydroplaning speeds are investigated, which is a key factor of hydroplaning. Results indicated that the hydroplaning speed increases with the increment of inflation pressure; the hydroplaning speed decreases with the increment of the footprint aspect ratio.

Application of particle trajectory model in 1D planar ejection

A simple one-dimensional planar model for ejection was set up based on experiments. And numerical simulation was performed on this model with particle trajectory model method. An Eulerian finite volume method was conducted to resolve gas field. And Lagrangian method was imposed to track each particle. The interaction between gas and particles was responded as source terms in governing equations which were induced by forces. The effects of total spraying mass, particle size and other factors on the mixture of particles and gas were investigated. The spatial distributions of particle mass and velocity at different time were presented. The result shows that the numerical results are qualitatively consistent to those of experiments.

Braking Distance Prediction by Hydroplaning Analysis of 3-D Patterned Tire Model

In this paper, we present a wet-road braking distance estimate for the vehicles equipped with ABS (Anti-lock Brake System). In order to effectively compute the interval-wise braking times and the resulting total braking distance, we divide the entire speed interval at braking into finite number of uniform sub-intervals and apply the energy conservation law to individual sub-intervals. The proposed method is based on a numerical-analytical approach such that the frictional energy loss of the patterned tire is computed by 3-D hydroplaning analysis while the other at the disc pad is analytically derived. The hydroplaning simulation is performed by generally coupling an Eulerian finite volume method and an explicit Lagrangian finite element method. The operation of ABS is numerically implemented by controlling the tire angular velocity such that the preset tire slip ratio on the wet road is maintained. Numerical results are presented to illustrative and verify the the proposed numerical estimate.

A wet‐road braking distance estimate utilizing the hydroplaning analysis of patterned tire

AbstractA wet‐road braking distance estimate for the vehicles equipped with ABS (anti‐lock brake system) is presented in this paper. The entire speed interval at braking is divided into several uniform sub‐intervals, and the energy conservation law is applied to individual sub‐intervals to predict the intervalwise braking times and the resulting velocity profile at braking and the total braking distance. The proposed method is based on a numerical‐analytical approach such that the frictional energy loss of the patterned tire is computed by 3‐D hydroplaning analysis while the other at the disc pad is analytically derived. The operation of ABS is numerically implemented by controlling the tire angular velocity such that the preset tire slip ratio on the wet road is maintained. The tire hydroplaning is analysed by generally coupling an Eulerian finite volume method and an explicit Lagrangian finite element method. Illustrative numerical experiment is presented to support the validity of the proposed estimate. Copyright © 2006 John Wiley & Sons, Ltd.

A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method

AbstractThis paper describes and compares two vorticity‐based integral approaches for the solution of the incompressible Navier–Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well‐established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity‐based methods. Copyright © 2005 John Wiley & Sons, Ltd.

Lagrangian 보오텍스 방법에서의 압력장 계산

In the Lagrangian vortex particle method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations, a numerical scheme for calculating pressure fields is presented. Implementation of the numerical method is directly connected with the well-established surface panel methods, just by dealing with the dynamic coupling among vorticity field. Assuming the vorticity and the velocity fields are to be calculated in time domain analysis, the pressure calculation for a complete set of solution at present time step is performed in a similar way to the one used in the Eulerian description. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsive started circular cylinder for Reynolds number 550. The comparative study with the Eulerian finite Volume method provides an extensive understanding and application of the mesh-free Lagrangian vortex methods for numerical simulation of viscous flows around arbitrary bodies of general shape.

An Adaptive Grid Eulerian Method for the Computation of Free Surface Flows

A numerical scheme for the prediction of free surface flows is presented and investigated. The method is based on an adaptive grid Eulerian finite-volume method, where non-orthogonal boundary-fitted moving grids are employed to follow the free surface. The underlying flow solver consists in a pressure-correction scheme of SIMPLE type with multigrid acceleration, which is iteratively combined with the moving grid technique. Several numerical examples are considered to illustrate the capabilities of the approach.

Scalable computations in penetration mechanics

This paper presents an overview of an explicit message-passing paradigm for a Eulerian finite volume method for modeling solid dynamics problems involving shock wave propagation, multiple materials, and large deformations. Three-dimensional simulations of high-velocity impact were conducted on the IBM SP2, the SGI Power Challenge Array, and the SGI Origin 2000. The scalability of the message-passing code on distributed-memory and symmetric multiprocessor architectures is presented and compared to the ideal linear performance.