A High-Accuracy Curve Boundary Recognition Method Based on the Lattice Boltzmann Method and Immersed Moving Boundary Method

Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Lattice Boltzmann(LBM)and the immersion boundary method based on solid ratio(IMB)have limitations in identifying custom curved boundaries.Meanwhile,IBM based on velocity correction(IBM-VC)suffers from inaccuracies and numerical instability.Therefore,this study introduces a high-accuracy curve boundary recognition method(IMB-CB),which identifies boundary nodes by moving the search box,and corrects the weighting function in LBM by calculating the solid ratio of the boundary nodes,achieving accurate recognition of custom curve boundaries.In addition,curve boundary image and dot methods are utilized to verify IMB-CB.The findings revealed that IMB-CB can accurately identify the boundary,showing an error of less than 1.8%with 500 lattices.Also,the flow in the custom curve boundary and aerodynamic characteristics of the NACA0012 airfoil are calculated and compared to IBM-VC.Results showed that IMB-CB yields lower lift and drag coefficient errors than IBM-VC,with a 1.45%drag coefficient error.In addition,the characteristic curve of IMB-CB is very stable,whereas that of IBM-VC is not.For the moving boundary problem,LBM-IMB-CB with discrete element method(DEM)is capable of accurately simulating the physical phenomena of multi-moving particle flow in complex curved pipelines.This research proposes a new curve boundary recognition method,which can significantly promote the stability and accuracy of fluid-solid interaction simulations and thus has huge applications in engineering.

A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

Aerodynamic performance of high-turning curved compressor cascade with boundary layer suction

The impact of boundary layer suction on the aerodynamic performance of a high-turning compressor cascade was numerically simulated and discussed.The aerodynamic performance of a curved and a straight cascade with and without boundary layer suction were comparatively studied at several suction flow rates.The results showed that boundary layer suction dramatically improved the flow behavior within the flow passage.Moreover,higher loading over the whole blade height,lower total pressure loss,and higher passage throughflow were achieved with a relatively small amount of boundary layer removal.The integration of curved blade and boundary layer suction contributed to better aerodynamic performance than the cascades with only curved blade or boundary layer suction used,and the more favorable effect resulted from the weakening of the three dimensional effects of the boundary layer close to the endwalls.

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.

Strengthening-softening transition and maximum strength in Schwarz nanocrystals

Recently,a Schwarz crystal structure with curved grain boundaries(GBs)constrained by twin-boundary(TB)networks was discovered in nanocrystalline Cu through experiments and atomistic simulations.Nanocrystalline Cu with nanosized Schwarz crystals exhibited high strength and excellent thermal stability.However,the grainsize effect and associated deformation mechanisms of Schwarz nanocrystals remain unknown.Here,we performed large-scale atomistic simulations to investigate the deformation behaviors and grain-size effect of nanocrystalline Cu with Schwarz crystals.Our simulations showed that similar to regular nanocrystals,Schwarz nanocrystals exhibit a strengthening-softening transition with decreasing grain size.The critical grain size in Schwarz nanocrystals is smaller than that in regular nanocrystals,leading to a maximum strength higher than that of regular nanocrystals.Our simulations revealed that the softening in Schwarz nanocrystals mainly originates from TB migration(or detwinning)and annihilation of GBs,rather than GB-mediated processes(including GB migration,sliding and diffusion)dominating the softening in regular nanocrystals.Quantitative analyses of simulation data further showed that compared with those in regular nanocrystals,the GB-mediated processes in Schwarz nanocrystals are suppressed,which is related to the low volume fraction of amorphous-like GBs and constraints of TB networks.The smaller critical grain size arises from the suppression of GB-mediated processes.

Performance Investigation of 2D Lattice Boltzmann Simulation of Forces on a Circular Cylinder

The lattice Boltzmann method (LBM) is employed to simulate the uniform flow past a circular cylinder. The performance of the two-dimensional LBM model on the prediction of force coefficients and vortex shedding frequency is investigated. The local grid refinement technique and second-order boundary condition for curved walls are applied in the calculations. It is found that the calculated vortex shedding frequency, drag coefficient and lift coefficient are consistent with experimental results at Reynolds nu...

A second order isoparametric finite element method for elliptic interface problems

A second order isoparametric finite element method （IPFEM） is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.

A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

For steady Euler equations in complex boundary domains,high-order shockcapturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian grids to achieve uniform high-order accuracy.In this paper,we utilize a fifth-order finite difference hybrid WENO scheme to simulate steady Euler equations,and the same fifth-order WENO extrapolation methods are developed to handle the curved boundary.The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary,involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure.Both equivalent expressions involving curvature and numerical differentiation are utilized to transform the tangential derivatives along the curved solid wall boundary.This hybrid WENO scheme is robust for steady-state convergence and maintains high-order accuracy in the smooth region even with the solid wall boundary condition.Besides,the essentially non-oscillation property is achieved.The numerical spectral analysis also shows that this hybrid WENO scheme has low dispersion and dissipation errors.Numerical examples are presented to validate the high-order accuracy and robust performance of the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.

Constrained multi-degree reduction of triangular Bézier surfaces

This paper proposes and applies a method to sort two-dimensional control points of triangular Bezier surfaces in a row vector. Using the property of bivariate Jacobi basis functions, it further presents two algorithms for multi-degree reduction of triangular Bezier surfaces with constraints, providing explicit degree-reduced surfaces. The first algorithm can obtain the explicit representation of the optimal degree-reduced surfaces and the approximating error in both boundary curve constraints and corner constraints. But it has to solve the inversion of a matrix whose degree is related with the original surface. The second algorithm entails no matrix inversion to bring about computational instability, gives stable degree-reduced surfaces quickly, and presents the error bound. In the end, the paper proves the efficiency of the two algorithms through examples and error analysis.

POSITIONAL ERROR CURVES BAND OF A PLANAR LINE SEGMENT WITHIN GISs

In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the general boundary curve formula of that band was derived. Secondly, the visualizing error curves bands were realized through three exam- ples. Finally,area index has been examined by comparing numerical results from error curves band and error ellipes band.

Lattice Boltzmann simulation of flow around two,three and four circular cylinders in close proximity

Cross-flows around two,three and four circular cylinders in tandem,side-by-side,isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5D,where D is the identical circular cylinder diameter.The wake patterns,pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases.The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures,which are interesting,complex and useful for practical applications.This study provides a useful database to validate the simplicity,accuracy and robustness of the Lattice Boltzmann method.

Influence of equiatomic Zr/(Ti,Nb)substitution on microstructure and ultra-high strength of(Ti,Zr,Nb)C medium-entropy ceramics at 1900℃

High-temperature mechanical properties of medium-entropy carbide ceramics have attracted significant attention.Tailoring the microstructure is an effective way to improve these high-temperature mechanical properties,which can be affected by the evolution of the enthalpy and entropy,as well as by lattice distortion and sluggish diffusion.In this study,the effects of equiatomic Zr/(Ti,Nb)substitution(Zr content of 10-40 at%)on the microstructure and high-temperature strength of(Ti,Zr,Nb)C medium-entropy ceramics were investigated.The grain size of the(Ti,Zr,Nb)C medium-entropy ceramics was refined from 9.4±3.7 to 1.1±0.4μm with an increase in the Zr content from 10.0 to 33.3 at%.A further increase in the Zr content to 40 at%resulted in a slight increase in the grain size.At 1900℃,the(Ti,Zr,Nb)C medium-entropy ceramics with the Zr contents of 33.3 and 40 at%exhibited ultra-high flexural strengths of 875±43 and 843±71 MPa,respectively,which were higher than those of the transition metal carbides previously reported under similar conditions.Furthermore,relatively smooth grain boundaries,which were detected at a test temperature of 1000℃,transformed into curved and serrated boundaries as the temperature increased to 1900℃,which may be considered the primary reason for the improved high-temperature flexural strength.The associated mechanism was analyzed and discussed in detail.