A Parallel,Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids

A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids.In this method,an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring,interface-sharing cells.The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution.The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple,accurate,consistent,and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations.A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method,which is based on domain partitioning and Single Program Multiple Data(SPMD)parallel programming model.The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy,efficiency,robustness,and versatility.The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method,at the same time providing a better performance than the third order DG method,in terms of both computing costs and storage requirements.

Terrain reconstruction from Chang'e-3 PCAM images

The existing terrain models that describe the local lunar surface have limited resolution and accuracy, which can hardly meet the needs of rover navigation,positioning and geological analysis. China launched the lunar probe Chang＇e-3 in December, 2013. Chang＇e-3 encompassed a lander and a lunar rover called ＂Yutu＂（Jade Rabbit）. A set of panoramic cameras were installed on the rover mast. After acquiring panoramic images of four sites that were explored, the terrain models of the local lunar surface with resolution of 0.02 m were reconstructed. Compared with other data sources, the models derived from Chang＇e-3 data were clear and accurate enough that they could be used to plan the route of Yutu.

The effect of catalyst layer design on catalyst utilization in PEMFC studied via stochastic reconstruction method

Catalyst utilization is an important determinant of proton exchange membrane fuel cell performance,and increasing the catalyst utilization is one of the most critical approaches to reducing the catalyst loading in PEMFC.4-phase stochastic reconstruction method based on the variable-resolution Quartet Structure Generation Set(QSGS)algorithm is utilized to elucidate the influence of different parameters of electrode preparation,including the porosity,the dispersion degree of carbon agglomerate,ionomer content,and carbon support size,on the catalyst utilization in the catalyst layer.It was found that there exist optimal values for the porosity,dispersion degree of carbon agglomerate,ionomer content,and carbon support sizes in CLs and any deviations from these optimal values would lead to transport issues of electron,proton and mass within CLs.Taking electron,proton and mass transport into consideration simultaneously,the optimal Pt utilization is 46.55%among 48 cases in this investigation,taken at the carbon support diameter of 40 nm,the porosity of 0.4,the agglomerate spatial density of 25μm^(−3) and I/C at 0.7.The selection of porosity,ultrasonic dispersion technique and ionomer content for conventional electrode preparation requires compromises on mass,electron and proton transport,leading to catalyst utilization in CLs hardly exceeding 50%.Therefore,the next generation of catalyst layer design and preparation technology is desired.

A robust compact least-squares reconstruction method for compressible turbulent flow simulations of complex configurations

For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.

Implicit Quadrature-Free Direct Reconstruction Method for Efficient Scale-Resolving Simulations

The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.

An adaptive image sparse reconstruction method combined with nonlocal similarity and cosparsity for mixed Gaussian-Poisson noise removal

Compressed sensing(CS) has achieved great success in single noise removal. However, it cannot restore the images contaminated with mixed noise efficiently. This paper introduces nonlocal similarity and cosparsity inspired by compressed sensing to overcome the difficulties in mixed noise removal, in which nonlocal similarity explores the signal sparsity from similar patches, and cosparsity assumes that the signal is sparse after a possibly redundant transform. Meanwhile, an adaptive scheme is designed to keep the balance between mixed noise removal and detail preservation based on local variance. Finally, IRLSM and RACoSaMP are adopted to solve the objective function. Experimental results demonstrate that the proposed method is superior to conventional CS methods, like K-SVD and state-of-art method nonlocally centralized sparse representation(NCSR), in terms of both visual results and quantitative measures.

A study on improving anti-interference capability of inversion method reconstructing layered sea bottom parameters

The remote measurement of the vertical distribution of acoustical parameters of the sea bottom is an inverse method in acoustics. The existing methods can be divided into two types: the wave method and the ray method. The former usually does not apply to cases with discontinuity in acoustical parameter profiles[1] , whereas the latter usually ignores the contributions made by multiple reflections, resulting in the appearance of pseudo interfaces. However, under certain practical circumstances, the ray method can produce satisfactory results[2,3]. In this paper, at first we use the conception of equitime layer thickness to obtain the pulse response iteration method. The anti-interference capability of this method is poor. In order to improve this capability, we develope the sample iteration method and the sample-averaging iteration method. The sample-averaging iteration method introduces a way of statistical averaging, which can further improve the anti-interference capability.

Region stepwise reconstruction method based on two source–detector-separation groups for reconstructing background optical properties of two-layered slab sample

The accuracy of the background optical properties has a considerable effect on the quality of reconstructed images in near-infrared functional brain imaging based on continuous wave diffuse optical tomography（CW-DOT）. We propose a region stepwise reconstruction method in CW-DOT scheme for reconstructing the background absorption and reduced scattering coefficients of the two-layered slab sample with the known geometric information. According to the relation between the thickness of the top layer and source– detector separation, the conventional measurement data are divided into two groups and are employed to reconstruct the top and bottom background optical properties, respectively. The numerical simulation results demonstrate that the proposed method can reconstruct the background optical properties of two-layered slab sample effectively. The region-of-interest reconstruction results are better than those of the conventional simultaneous reconstruction method.

Analysis of magnetotail flux rope events by ARTEMIS observations

Three earthward flowing magnetic flux ropes observed in the duskside plasma sheet at geocentric solar magnetospheric coordinate X~–55 Re by P1 and P2 of acceleration,reconnection,turbulence and electrodynamics of moon’s interaction with the sun mission during 13:00–15:00 UT on July 3,2012,were studied.The morphologies of the flux ropes were studied in detail based on Grad-Shfranov reconstruction method and electronic pitch angle distribution data.It is found that(1)the flux rope cross-sectional dimensions are 1.0 Re×0.78 Re,1.3 Re×0.78 Re,and 2.5 Re×1.25 Re,respectively.The magnetic field lines were asymmetric about the center with field line compression on both sides of the current sheet at the leading region;(2)the electron energy flux data presented asymmetry with larger electron flux and lower temperature in the precursor region.The flux ropes were blocked by the resistance of compressed particle density in the front central plasma sheet and the enhanced magnetic field on its sides;and(3)it is found that the flux rope has a layered structure.From inside out,event 1 can be divided into three regions,namely electronic depletion core region,closed field line region,and the caudal area possible with fields connected with the ionosphere.It suggests that the flux ropes cannot merge with the tail magnetic field lines near the lunar orbit.Especially,the flux rope asymmetrical shape reflects the different reconnection processes that caused it on both sides of the magnetic structure.The events shown in this paper support the multiple X-line magnetic reconnection model for flux ropes with in situ observations.

On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws

This paper is concerned with a new version of the Osher-Solomon Riemann solver and is based on a numerical integration of the path-dependent dissipation matrix.The resulting scheme is much simpler than the original one and is applicable to general hyperbolic conservation laws,while retaining the attractive features of the original solver:the method is entropy-satisfying,differentiable and complete in the sense that it attributes a different numerical viscosity to each characteristic field,in particular to the intermediate ones,since the full eigenstructure of the underlying hyperbolic system is used.To illustrate the potential of the proposed scheme we show applications to the following hyperbolic conservation laws:Euler equations of compressible gasdynamics with ideal gas and real gas equation of state,classical and relativistic MHD equations as well as the equations of nonlinear elasticity.To the knowledge of the authors,apart from the Euler equations with ideal gas,an Osher-type scheme has never been devised before for any of these complicated PDE systems.Since our new general Riemann solver can be directly used as a building block of high order finite volume and discontinuous Galerkin schemes we also show the extension to higher order of accuracy and multiple space dimensions in the new framework of PNPM schemes on unstructured meshes recently proposed in[9].