Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method

Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.

Numerical Simulation of Flow Field in Tidal Estuary Using Body-Fitted Coordinate System

On the basis of the physical mechanism, a body-fitted coordinate system is developed. By using this system the boundaries in simulation and in real are fitted well, and simulation with great accuracy is achieved. A computation example indicates that compared to traditional two-dimensional computation methods, the body-fitted simulation has an advantange of better coincidence with the real and can be adopted in simulating flow fields in tidal estuaries.

Feature study of body-fitted Cartesian grids used in casting numerical simulation

A type of mesh called a body-fi tted Cartesian mesh,very different from the traditional structured body-fi tted mesh,is established.At f irst,the right parallelepiped mesh is generated,then,a feature analysis is done on the cross sections.These cross sections are the intersections of the casting shape with the right parallelepiped grids(under the Cartesian coordinate system).On the basis of the feature analysis,two sorts of body-f itted boundary grids,shape-keeping grids and shape-distortion grids,are def ined.Shape-distortion grids can be removed or weaken by increasing the number of grids or moving the coordinates of the mesh generation region,so actually the body-fitted Cartesian mesh generation is to get shape-keeping grids.A shape-keeping grid mainly consists of two sorts of surfaces(I type face and II type face),and each of them is joined by two types of points(I type point and II type point).If only these two types of points were given,the shape-keeping mesh would be constructed.In this paper,the cases of the above two boundary grids being generated were discussed.An algorithm was put forward to get the shape-keeping grids.Several body-fi tted Cartesian meshes generated on castings show the validity of the algorithm.The mesh generation examples show that the body-fi tted Cartesian mesh is more excellent than the right parallelepiped mesh in aspects of decreasing grids number and being closer to the shape of the casting solid.

A CAD-compatible body-fitted particle generator for arbitrarily complex geo-metry and its application to wave-structure interaction

Generating body-fitted particle distribution for arbitrarily complex geometry underpins the applications of particle-based method to engineering and bioengineering and is highly challenging,and thus hinders the potential of particle methods.In this paper,we present a new computer-aided design(CAD)compatible body-fitted particle generator,termed as CAD-BPG,for arbitrarily complex 3-D geometry.By parsing a CAD model,the present method can accurately tackle arbitrarily complex geometry representation and describe the corresponding geometry surface by constructing an implicit zero level-set function on Cartesian background mesh.To achieve a body-fitted and isotropic particle distribution,physics-driven relaxation process with surface bounding governed by the transport-velocity formulation of smoothed particle hydrodynamics(SPH)methodology is conducted to characterize the particle evolution.A set of examples,ranging from propeller,stent structures and anatomical heart models,show simplicity,accuracy and versatility of the present CAD-BPG for generating body-fitted particle distribution of arbitrarily complex 3-D geometry.Last but not least,the present CAD-BPG is applied for modeling wave-structure interaction,where wave interaction with an oscillating wave surge converter is studied,and the results show that the present method not only provides an efficient and easy-to-implement pre-processing tool for particle-based simulation but also improves the numerical accuracy compared with lattice particle distribution.Consequently,the propose CAD-BPG sheds light on simulating real-world applications by particle-based methods for researchers and engineers.

COMPRESSIBLE FLOW SIMULATION AROUND AIRFOIL BASED ON LATTICE BOLTZMANN METHOD

The flow around airfoil NACA0012 enwrapped by the body-fitted grid is simulated by a coupled doubledistribution-function （DDF） lattice Boltzmann method （LBM） for the compressible Navier-Stokes equations. Firstly, the method is tested by simulating the low Reynolds number flow at Ma =0. 5,a=0. 0, Re=5 000. Then the simulation of flow around the airfoil is carried out at Ma：0. 5, 0. 85, 1.2; a=-0.05, 1.0, 0.0, respectively. And a better result is obtained by using a local refined grid. It reduces the error produced by the grid at Ma=0. 85. Though the inviscid boundary condition is used to avoid the problem of flow transition to turbulence at high Reynolds numbers, the pressure distribution obtained by the simulation agrees well with that of the experimental results. Thus, it proves the reliability of the method and shows its potential for the compressible flow simulation. The suecessful application to the flow around airfoil lays a foundation of the numerical simulation of turbulence.

THREE—DIMENSIONAL GAS TURBINE COMBUSTOR PERFORMANCE MODELING

Numerical analysis of three-dimensional(3-D)two-phase reacting flowfield in an annular combustor wity the dump diffuser is developed in arbitrary curvilinear coordi-nates.Combustor performances are estimated by the em-pirical-analytical desing method.Ths influence of three inlet velocity profiles of the prediffuser and two operating conditions on combustor preformance and flow character-istic is predicted.

Heat Transfer Characteristic of Molten Pool for Twin-Roll Strip Casting

Body-fitted coordinate transformation equation was deduced and used to generate the body-fitted grids of molten pool for twin-roll strip casting.The orthogonality of the grids on the boundary was modified by adjusting source item.The energy equation and the boundary conditions were transformed from physical space to computational space.The velocity field model proposed by Hirohiko Takuda was used to calculate the temperature field of molten steel,and the influence of technical factors was also discussed.

Study on accuracy of casting flow simulation

In the field of casting flow simulation, the application of body-fitted coordinate(BFC) has not been widely used due to the difficulty and low efficiency of grid generation, despite the availability of good quality analysis results. Cartesian coordinates, on the other hand, have been used predominantly in casting process simulations because of their relatively easy and fast grid generation. However, Cartesian grid systems cannot obtain accurate results because they cannot express the geometries properly. In this study, Cut Cell method was applied to solve this problem. The three-dimensional incompressible viscous governing equation was analyzed using a function defined for the volume and area of the casting in the cutting cell. Using the Cut Cell method, accurate flow analysis results were also obtained in the Cartesian grid systems. The tests of simple shape and the applications of actual casting product have been tried with Cut Cell method.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS IN A CUT-OFF VALVE AND ANALYSIS OF FLOW CHARACTERISTICS IN PIPE

The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system, the discretised equations were solved by the SIMPLESTalgorithm. The numerical result of a cut-off valve with curved inlet shows the flow characteristicsand the main cause of energy loss when fluid flows through a valve. And then, the boundaries ofvalve were modified in order to reduce the energy loss. The computational results of modified valveshow that the numerical value of turbulent kinetic energy is lower, and that the modified design ofthe 3-D valve boundaries is much better. The analysis of the result also shows that RNG k-εturbulence model can successfully be used to predict the 3-D turbulent separated flows and thesecondary flow inside valve pipes.

Numerical Study of an Annular Gas Turbine Combustor with Dump Diffuser

A general numerical method is presented for calculating steady three-dimensional and two-phase turbulent reactive flows with a nonstaggered body-fitted coordinate system in an annular gas turbine combustor with the dump diffuser. The modified two-equation model and the EDC turbulent combustion model are used for the gas phase. The liquid phase equations are solved in a Lagrangian frame of reference by PSIC algorithm. The effect of different velocity profiles at the entry of the prediffuser on combustor flow characteristics is calculated.

Numerical research on lid-driven cavity flows using a three-dimensional lattice Boltzmann model on non-uniform meshes

A lattice Boltzmann model combined with curvilinear coordinate is proposed for lid-driven cavity three-dimensional (3D) flows. For particle velocity distribution, the particle collision process is performed in physical domain, and the particle streaming process is carried out in the corresponding computational domain, which is transferred from the physical domain using interpolation method. For the interpolation calculation, a second-order upwind interpolation method is adopted on internal lattice nodes in flow fields while a second-order central interpolation algorithm is employed at neighbor-boundary lattice nodes. Then the above-mentioned model and algorithms are used to numerically simulate the 3D flows in the lid-driven cavity at Reynolds numbers of 100, 400 and 1000 on non-uniform meshes. Various vortices on the x-y, y-z and x-z symmetrical planes are successfully predicted, and their changes in position with the Reynolds number increasing are obtained. The velocity profiles of u component along the vertical centerline and w component along the horizontal centerline are both in good agreement with the data in literature and the calculated results on uniform meshes. Besides, the velocity vector distributions on various cross sections in lid-driven cavity predicted on non-uniform meshes are compared with those simulated on uniform meshes and those in the literature. All the comparisons and validations show that the 3D lattice Boltzmann model and all the numerical algorithms on non-uniform meshes are accurate and reliable to predict effectively flow fields.

AN APPROACH TO THE STUDY OF TRANSVERSE MIXING IN NATURAL RIVERS

A numerical model of transverse mixing in natural rivers has been presented by using the body-fitted coordinate systems,which is capable of describing the complex flow and mixing characteristics of rivers.To study the validity and to illustrate the applicability of this model,field measurement date in the Gan River near Nanchang have been used to compare the numerical results.

Grid Generation and Numerical Analysis of Multi-Stream Flow in the Complex Channel with a Forced Mixer Lobe

The co-located grid, SIMPLEC and Chen-Kim modified k - E turbulence model are applied to investigate numerically the multi-stream flow and temperature fields in the complex channel with a forced mixer lobe at room temperature and at elevated temperature. The body-fitted coordinate grids are generated respectively in sub-domains according to the shapes of the channel by solving Poisson’s equations to compose the whole grid of the domain. The large viscosity, linear and simultaneous under-relaxation factors are used to solve the coupling of fluid and solid. The solid grid is complemented at the upper inlet of the secondary flow to keep the same node number at the inlet and at double-wall sub-domains. The numerical results and experimental data show good agreement at room temperature. It is illustrated that the cooling air ejected into the slot between the double plates decreases the temperature of the wall.

Numerical Simulation of Natural Convection in Circular Enclosures with Inner Polygonal Cylinders,with Confirmation by Experimental Results

Numerical computations are performed for the natural convection in circular enclosures with inner polygonal cylinders.The polygon surface and the outer envelope are at constant but different temperatures,A body-fitted coordinate system is used,The coordinate system is generated via simple algebraic equations.The transformed governing equations are discretized on a control volume basis with power-law finite difference scheme.The SIMPLE-like algorithm is used to deal with the linkage between pressure and velocities.The numerical results are compared with the experimental data available in the literature,and the agreement between the numerical and experimental results are very good.

Application of Lattice Boltzmann Method to Simulation of Compressible Turbulent Flow

The main goal of this paper is to develop the coupled double-distributionfunction(DDF)lattice Boltzmann method(LBM)for simulation of subsonic and transonic turbulent flows.In the present study,we adopt the second-order implicit-explicit(IMEX)Runge-Kutta schemes for time discretization and the Non-Oscillatory and NonFree-Parameters Dissipative(NND)finite difference scheme for space discretization.The Sutherland’s law is used for expressing the viscosity of the fluid due to considerable temperature change.Also,the Spalart-Allmaras(SA)turbulence model is incorporated in order for the turbulent flow effect to be pronounced.Numerical experiments are performed on different turbulent compressible flows around a NACA0012 airfoil with body-fitted grid.Our numerical results are found to be in good agreement with experiment data and/or other numerical solutions,demonstrating the applicability of the method presented in this study to simulations of both subsonic and transonic turbulent flows.