高速飞行弹丸诱导的三维爆轰波数值模拟

采用三维非定常化学反应控制方程组对驻定在带攻角高速飞行弹丸上的斜爆轰波流场进行了数值模拟。对流项和化学反应项采用时间分裂法,分别用TVD格式和基元反应模型进行处理。计算结果表明三维数值模拟可以更准确的描述弹丸飞行攻角对爆轰波的形成及结构的影响,是进一步研究超驱爆轰推进技术的重要手段。

UPWIND SCHEME FOR IDEAL 2-D MHD FLOWS BASED ON UNSTRUCTURED MESH

An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics （MHD） equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method （AUSM） scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.

2.5D induced polarization forward modeling using the adaptive finite-element method

The conventional finite-element（FE） method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization（IP）. In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.

A FVCOM-Based Unstructured Grid Wave, Current,Sediment Transport Model,I.Model Description and Validation

An effort was made to couple FVCOM (a three-dimensional (3D),unstructured grid,Finite Volume Coastal Ocean Model) and FVCOM-SWAVE (an unstructured grid,finite-volume surface wave model) for the study of nearshore ocean processes such as tides,circulation,storm surge,waves,sediment transport,and morphological evolution.The coupling between FVCOM and FVCOM-SWAVE was achieved through incorporating 3D radiation stress,wave-current-sediment-related bottom boundary layer,sea surface stress parameterizations,and morphology process.FVCOM also includes a 3D sediment transport module.With accurate fitting of irregular coastlines,the model provides a unique tool to study sediment dynamics in coastal ocean,estuaries,and wetlands where local geometries are characterized by inlets,islands,and intertidal marsh zones.The model was validated by two standard benchmark tests: 1) spectral waves approaching a mild sloping beach and 2) morphological changes of seabed in an idealized tidal inlet.In Test 1,model results were compared with both analytical solutions and laboratory experiments.A further comparison was also made with the structured grid Regional Ocean Model System (ROMS),which provides an insight into the performance of the two models with the same open boundary forcing.

Unstructured Grid Immersed Boundary Method for Numerical Simulation of Fluid Structure Interaction

This paper presents an improved unstructured grid immersed boundary method.The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain.The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain.The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS(volume of solid) method.A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph.The method is verified with flow past oscillating cylinder.

Three-dimensional forward modeling for the SBTEM method using an unstructured fi nite-element method

In this study,we propose a three-dimensional(3D)forward modeling algorithm of surface-to-borehole transient electromagnetic(SBTEM)fields based on an unstructured vector fi nite-element method to analyze the characteristics of SBTEM responses for complex geoelectrical models.To solve the double-curl diff usion equation for the electric fi eld,we use an unstructured tetrahedral mesh to discretize the model domain and select the unconditionally stable backward Euler scheme to discretize the time derivative.In our numerical experiments,we use a grounded wire as a transmitting source.After validating the algorithm’s eff ectiveness,we first analyze the diffusion characteristics and detectability of the electromagnetic field.After that,we focus our attention on the distribution and the cause of zero bands for Ex and dBy/dt components with the hope of guiding future field surveys.Finally,by simulating diff erent models,we analyze the capability of the SBTEM method in detecting typical mineral veins so that we can provide a reference for mineral resource exploration in the deep earth.

Application of Factor Difference Scheme to Solving Discrete Flow Equations Based on Unstructured Grid

A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorthogonal diffusion items generated by the scheme in discrete equations is provided.The Delaunay triangulation method is improved to generate the unstructured grid.The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow.The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively.In the former case,a good agreement is achieved in the main velocity and drag coefficient curve.In the latter case,the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment.It is indicated that the factor difference scheme is of higher accuracy,and feasible to be applied to Navier-Stokes equation.

The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Effects of mesh style and grid convergence on numerical simulation accuracy of centrifugal pump

In order to evaluate the effects of mesh generation techniques and grid convergence on pump performance in centrifugal pump model, three widely used mesh styles including structured hexahedral, unstructured tetrahedral and hybrid prismatic/tetrahedral meshes were generated for a centrifugal pump model. And quantitative grid convergence was assessed based on a grid convergence index(GCI), which accounts for the degree of grid refinement. The structured, unstructured or hybrid meshes are found to have certain difference for velocity distributions in impeller with the change of grid cell number. And the simulation results have errors to different degrees compared with experimental data. The GCI-value for structured meshes calculated is lower than that for the unstructured and hybrid meshes. Meanwhile, the structured meshes are observed to get more vortexes in impeller passage.Nevertheless, the hybrid meshes are found to have larger low-velocity area at outlet and more secondary vortexes at a specified location than structured meshes and unstructured meshes.

Reverse time migration imaging of tunnels via the finite element method using an unstructured mesh

Wavefield extrapolation is critical in reverse time migration(RTM).The finite diff erence method is primarily used to achieve wavefi eld extrapolation in case of the RTM imaging of tunnels.However,complex tunnel models,including those for karsts and fault fracture zones,are constructed using regular grids with straight curves,which can cause numerical dispersion and reduce the imaging accuracy.In this study,wavefi eld extrapolation was conducted for tunnel RTM using the finite element method,wherein an unstructured mesh was considered to be the body-fi tted partition in a complex model.Further,a Poynting vector calculation equation suitable for the unstructured mesh considered in the fi nite element method was established to suppress the interference owing to low-frequency noise.The tunnel space was considered during wavefi eld extrapolation to suppress the mirror artifacts based on the fl exibility of mesh generation.Finally,the infl uence of the survey layouts(one and two sidewalls)on the tunnel imaging results was investigated.The RTM results obtained for a simple tunnel model with an inclined interface demonstrate that the method based on unstructured meshes can effectively suppress the low-frequency noise and mirror artifacts,obtaining clear imaging results.Furthermore,the two-sidewall tunnel survey layout can be used to accurately obtain the real position of the inclined interface ahead of the tunnel face.The complex tunnel numerical modeling and actual data migration results denote the eff ectiveness of the fi nite element method in which an unstructured mesh is used.

Numerical Simulation of Seawater Intrusion from Estuary into River Using a Coupled Modeling System

One of the most important causes of the freshwater shortage in estuarine area is the increasing seawater intrusion into the river.To simulate seawater intrusion properly,two important factors should be considered.One is the bidirectional and time-dependent coupling effects between river discharges and tidal forces.The other is the three-dimensional and stratified structure of dynamic processes involved.However,these two factors have rarely been investigated simultaneously,or they were often simplified in previous researches,especially for the estuary connected with an upstream river network through multiple outlets such as the Pearl River Estuary(PRE).In order to consider these two factors,a numerical modeling system,which couples a one-dimensional river network model with a three-dimensional unstructured-grid Finite-Volume Coastal Ocean Model(FVCOM),has been developed and successfully applied to the simulation of seawater intrusion into rivers emptying into the PRE.By treating the river network with a one-dimensional model,computational efficiency has been improved.With coupling 1D and 3D models,the specification of upstream boundary conditions becomes more convenient.Simulated results are compared with field measured data.Good agreement indicates that the modeling system may correctly capture the physical processes of seawater intrusion into rivers.

Installation position determination of wind speed sensors on steel pole along a high-speed railway

In order to consider the influence of steel pole on the measurement of wind speed sensors and determinate the installation position of wind speed sensors, the flow field around wind speed sensors was investigated. Based on the three-dimensional steady Reynolds-averaged Navier-Stokes equations and k-ε double equations turbulent model, the field flow around the wind speed sensor and the steel pole along a high-speed railway was simulated on an unstructured grid. The grid-independent validation was conducted and the accuracy of the present numerical simulation method was validated by experiments and simulations carried out by previous researchers. Results show that the steel pole has a significant influence on the measurement results of wind speed sensors. As the distance between two wind speed sensors is varied from 0.3 to 1.0 m, the impact angles are less than ±20°, it is proposed that the distance between two wind speed sensors is 0.8 m at least, and the interval between wind speed sensors and the steel pole is more than 1.0 m with the sensors located on the upstream side.

Recent Advances to Change the Standards in Designing Hulls in Waves, a Validation Using an Efficient SWENSE Level-Set Approach

This paper presents recent naval applications of the SWENSE （Spectral Wave Explicit Navier-Stokes Equations） approach implemented for the first time with high order fully unstructured schemes and an efficient level-set method to capture free surface flows around realistic hull geometries. Numerical simulations in waves and/or viscous flows still lead generally to very large CPU times because of grid requirements to ensure a good propagation of incident waves in the meshed part of the fluid domain that makes unreachable any hull design optimization process in an industrial context. Furthermore, even if the SWENSE method clearly shows promising results in an academic context in both regular and irregular waves, the most recent publications still highlight several issues that remain unresolved up to now, e.g. poor scalability, diffusive wake pattern, non-versatile structured mesh approaches and only very few validation test cases are carried out on Wigley or DTMB 5415 hulls. In order to overcome those numerical difficulties and get an in-depth validation of the method on several cases in realistic wave conditions, a two and a half years＇ research project has been achieved involving several steps, starting by a set of dedicated model test experiments later used as reference for the validation of the method. The CFD commercial code ANANASTM used and developed in this research program is presented and validated in detail. The use of high order schemes on unstructured grids in combination with these SWENSE method and level-set approach offer to the maritime industry an innovative and state of the art method to achieve unequaled accuracy, low computation time and some unique advantages such as, amongst others, the end of the numerical wave propagation problems. The results of the validation were pleasing and can be considered as acceptable in general, with some challenges remaining to the solyed. Results obtained indicate that an optimization processes in waves in realistic conditions is now affordable in an industrial context.

Development and validation of a three-dimensional,wave-current coupled model on unstructured meshes

Using unstructured meshes provides great flexibility for modeling the flow in complex geomorphology of tidal creeks,barriers and islands,with refined grid resolution in regions of interest and not elsewhere.In this paper,an unstructured three-dimensional fully coupled wave-current model is developed.Firstly,a parallel,unstructured wave module is developed.Variations in wave properties are governed by a wave energy equation that includes wave-current interactions and dissipation representative of wave breaking.Then,the existing Finite-Volume Coastal Ocean Model(FVCOM) is modified to couple with the wave module.The couple procedure includes depth dependent wave radiation stress terms,Stokes drift,vertical transfer of wave-generated pressure transfer to the mean momentum equation,wave dissipation as a source term in the turbulence kinetic energy equation,and mean current advection and refraction of wave energy.Several applications are presented to evaluate the developed model.In particular the wind and wave-induced storm surge generated by Hurricane Katrina is investigated.The obtained results have been compared to the in situ measurements with respect to the wave heights and water level elevations revealing good accuracy of the model in reproduction of the investigated events.In a comparison to water level measurements at Dauphin Island,inclusion of the wave induced water level setup reduced the normalized root mean square error from 0.301 to 0.257 m and increased the correlation coefficient from 0.860 to 0.929.Several runs were carried out to analyze the effects of waves.The experiments show that among the processes that represent wave effects,radiation stress and wave-induced surface stress are more important than wave-induced bottom stress in affecting the water level.The Hurricane Katrina simulations showed the importance of the inclusion of the wave effects for the hindcast of the water levels during the storm surge.

A large-scale wave-current coupled module with wave diffraction effect on unstructured meshes

Based on the extended mild-slope equation,a large-scale wave module is developed.By combining the eikonal equation and the modified wave action equation,the wave model can account for diffraction in most situations such as in the lee of islands and breakwaters,and using unstructured meshes provides great flexibility for modelling the wave in the complex geomorphology of barriers and islands,also allowing for refinement of the grid resolution within computationally important domains.The numerical implementation of the module is based on the explicit second-order upwind finite-volume schemes in geographic space,the Flux-Corrected Transport(FCT)algorithm in frequency space and the implicit Crank-Nicolson method in directional space.The three-dimensional hydrodynamic module is then modified to couple with the wave model,where the wave readily provides the depth-dependent radiation stress and the wave-induced turbulence coefficient for the current fields,and the wave propagation takes into account the current-induced advection,refraction and diffraction of wave energy and the effect of water level.The applicability of the proposed model to calculate Snell’s Law,wave transformation over the breakwaters and the elliptic shoal,wave propagation over the rip current field and the undertow on a sloping beach is evaluated.Numerical results show that the present model makes better predictions of the near-shore wave propagation and complex three-dimensional(3D)near-shore circulation driven by the waves,considering analytical solutions and experimental values.

Coupling of wave and current numerical model with unstructured quadtree grid for nearshore coastal waters

This paper presents 2D wave-current interaction model for evaluating nearly horizontal wave-induced currents in the surf-zone and coastal waters.The hydrodynamic model is the two-dimensional depth-averaged nonlinear shallow water equations by using an unstructured non-staggered and multiple-level quadtree rectangular mesh,this mesh information is stored in simple data structures and it is easy to obtain a locally high resolution for important region.The intercell fluxes are computed based on the HLL(Harten-Lax-van Leer) approximate Riemann solver with shock capturing capability for computing the dry-to-wet interface of coastal line.The effects of pressure and gravity are included in source term in the model,this treatment can simplify the computation and eliminate numerical imbalance between source and flux terms.The wave model readily provides the radiation stresses that represent the shortwave-averaged forces in a water column for the hydrodynamic model and the wave model takes into account the effect of wave-induced nearshore currents and water level.The coupling model is applied to verify different experimental cases and real life case of considering the wave-current interaction.The calculated results agree with analytical solution,experimental and field data.The results show that the modeling approach presented herein should be useful in simulating the nearshore processes in complicated natural coastal domains.

Unsteady analysis of six-DOF motion of a 6:1 prolate spheroid in viscous fluid

Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.