A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.Th...A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.展开更多
In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order f...In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).展开更多
准确评估现有多源卫星降水产品的时空精度特征,可为长江流域的水资源高效开发利用奠定坚实的气象数据基础。利用长江流域191个气象站点1999—2019年逐日站点实测降水数据和TRMM(tropical rainfall measuring mission)、CMORPH(CPC MORPH...准确评估现有多源卫星降水产品的时空精度特征,可为长江流域的水资源高效开发利用奠定坚实的气象数据基础。利用长江流域191个气象站点1999—2019年逐日站点实测降水数据和TRMM(tropical rainfall measuring mission)、CMORPH(CPC MORPHing technique)、CHIRPS(climate hazards group infrared precipitation with station data)和PERSIANN_CDR(precipitation estimation from remotely sensed information using artificial neural networks climate data record)4种卫星降水产品,运用皮尔逊相关系数R、均方根误差E RMS和纳什效率系数E_(NS)等连续性指标评价卫星降水产品在长江流域时间和空间尺度上相对于站点降水的探测精度,并运用探测率P_(OD)、误报率R _(FA)和T_(S)评分3个分类评价指标衡量卫星降水产品对不同量级降水的捕捉能力。结果表明:在年尺度上,TRMM和CMORPH相对于CHIRPS和PERSIANN_CDR表现出更高的探测精度,而对于年降水量空间分布特征,仅有TRMM、CMORPH和CHIRPS能不同程度地准确反映;在月尺度上,TRMM和CMORPH对降水估计仍然具有较高精度,TRMM、CMORPH和CHIRPS在描述月降水空间分布方面在长江流域不同区域各具优势;在日尺度上,4种卫星降水产品对弱降水的捕捉能力均较强,对强降水探测能力则较差;在空间尺度上,4种卫星降水产品在日和月尺度上表现为高海拔地区精度较高,而年尺度上则无明显变化规律。总体而言,4种卫星降水产品中,TRMM和CMORPH在长江流域年、月、日不同时间尺度上更具优势,但在空间分布上,4种产品在不同地区差异显著。这一结论为进一步开发适用于长江流域的高时空分辨率降水融合产品奠定了研究基础。展开更多
基金funded by the research project STiMulUs,ERC Grant agreement no.278267Financial support has also been provided by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2022 attributed to DICAM of the University of Trento(Grant L.232/2016)the PRIN2017 project.The authors have also received funding from the University of Trento via the Strategic Initiative Modeling and Simulation.
文摘A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.
文摘In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).
文摘准确评估现有多源卫星降水产品的时空精度特征,可为长江流域的水资源高效开发利用奠定坚实的气象数据基础。利用长江流域191个气象站点1999—2019年逐日站点实测降水数据和TRMM(tropical rainfall measuring mission)、CMORPH(CPC MORPHing technique)、CHIRPS(climate hazards group infrared precipitation with station data)和PERSIANN_CDR(precipitation estimation from remotely sensed information using artificial neural networks climate data record)4种卫星降水产品,运用皮尔逊相关系数R、均方根误差E RMS和纳什效率系数E_(NS)等连续性指标评价卫星降水产品在长江流域时间和空间尺度上相对于站点降水的探测精度,并运用探测率P_(OD)、误报率R _(FA)和T_(S)评分3个分类评价指标衡量卫星降水产品对不同量级降水的捕捉能力。结果表明:在年尺度上,TRMM和CMORPH相对于CHIRPS和PERSIANN_CDR表现出更高的探测精度,而对于年降水量空间分布特征,仅有TRMM、CMORPH和CHIRPS能不同程度地准确反映;在月尺度上,TRMM和CMORPH对降水估计仍然具有较高精度,TRMM、CMORPH和CHIRPS在描述月降水空间分布方面在长江流域不同区域各具优势;在日尺度上,4种卫星降水产品对弱降水的捕捉能力均较强,对强降水探测能力则较差;在空间尺度上,4种卫星降水产品在日和月尺度上表现为高海拔地区精度较高,而年尺度上则无明显变化规律。总体而言,4种卫星降水产品中,TRMM和CMORPH在长江流域年、月、日不同时间尺度上更具优势,但在空间分布上,4种产品在不同地区差异显著。这一结论为进一步开发适用于长江流域的高时空分辨率降水融合产品奠定了研究基础。
