共查询到19条相似文献，搜索用时 46 毫秒
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在Newton迭代方法的基础上,对高阶精度间断Galerkin有限元方法(DGM)的时间隐式格式进行了研究. Newton迭代 法的优势在于收敛效率高效,并且定常和非定常问题能够统一处理,对于非定常问题无需引入双时间步策略. 为了避免大型矩阵的求逆,采用一步Gauss-Seidel迭代和Matrix-free技术消去残值Jacobi矩阵的上、下三角矩阵,从而只需计算和存储对角(块)矩阵. 对角(块)矩阵采用数值方法计算. 空间离散采用Taylor基,其优势在于对于任意形状的网格,基函数的形式是一致的,有利于在混合网格上推广. 利用该方法,数值模拟了Bump绕流和NACA0012翼型绕流. 计算结果表明,与显式的Runge-Kutta时间格式相比,隐式格式所需的迭代步数和CPU时间均在很大程度上得到减少,计算效率能够提高1～ 2个量级. 相似文献
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本文提出了一种任意曲线坐标系下的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组的隐式矢通量分裂格式的构造方法．该方法避开了近似因子分解、无矩阵运算,具有精度高、稳定性好、计算量少等优点．在扩压器进气道跨音流场的计算中,准确地捕获了激波,与实验比较,结果令人满意． 相似文献
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采用浸没边界格子Boltzmann (immersed boundary-lattice Boltzmann, IB-LB)模型执行动边界绕流数值模拟时,信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率.基于隐式扩散界面,一种改进的直接力格式IB-LB模型被提出.边界力表达式基于欧拉/拉格朗日变量同一性准则推导,转换矩阵描述的信息交互界面耦合了拉格朗日节点间的非同步运动.采用Richardson迭代数值求解关联边界力与无滑移速度约束的线性方程组,不仅克服了传统速度修正格式中矩阵求逆引起的计算效率问题,而且摆脱了算法稳定性对拉格朗日点分布的依赖.根据解析解已知的Taylor-Green涡流评估本文模型的数值模拟精度,结果表明改进的IB模型能够完整保留背景LB模型的二阶数值精度.静止圆柱和振荡圆柱绕流数值实验结果表明,当前模型在涉及复杂外形和运动界面的流动模拟中能够提供可靠的数值预测,满足力同一性的IB-LB模型能够有效抑制非定常流体力的伪物理震荡.波动翼型绕流模拟验证了当前模型的实用性,可在大变形柔性体流固耦合动力学问题中进一步推广. 相似文献
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基于玻尔兹曼模型方程的气体运动论统一算法(gas kinetic unified algorithm,GKUA) 给出了一种能模拟从连续流到自由分子流跨流域空气动力学问题的途径. 该算法采用传统计算流体力学技术将分子运动和碰撞解耦处理,若采用显式格式将受格式稳定条件限制,在模拟超声速流动尤其是近连续流和连续流区的流动时计算效率较低. 为了提高计算效率,扩展其工程实用性,采用上下对称高斯-赛德尔(LU-SGS) 方法和有限体积法构造了求解玻尔兹曼模型方程的隐式方法,同时在物理空间采用能处理任意连接关系的多块对接网格技术. 通过模拟近连续过渡区并排圆柱绕流问题,计算结果与直接模拟蒙特卡洛方法模拟值吻合较好,验证了该方法用于跨流域空气动力计算的可靠性与可行性. 相似文献
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基于混合网格Navier-Stokes方程的并行隐式计算方法研究 总被引：2，自引：0，他引：2
针对结构网格很难处理复杂外形和非结构网格无法计算具有边界层的粘性流动的缺点,发展了基于混合网格格点的隐式算法,成功地解决了在工程应用中难于处理的复杂外形粘性流场计算和效率问题。同时针对大规模的工程问题,发展了基于MPI通信技术的染色分层通讯并行计算方法。其中空间离散采用基于Roe格式发展的三阶迎风HLLEW(Harten-Lax-Van Leer-Einfeldt-Wada)或AUSM格式,湍流模型采用k??两方程湍流模型,时间推进考虑到LU-SGS并行等效较困难则采用基于DP-LUR(Data-Parallel Lower-Upper Relaxation)格式的隐式算法,计算CFL数可取到105量级,从2个到128个CPU的并行加速效率都保持在90%以上,大大提高了计算效率。算例对标模M6机翼模型流场进行计算,验证了方法的可靠性;然后对标模DLR-F6翼身组合体进行混合网格粘性与无粘计算结果进行比较,进一步验证混合网格方法;最后计算了DLR-WBNP外挂发动机翼身组合体模型,准确模拟了外挂和超临界机翼的相互干扰流动问题,采用4 CPU 16 CORE到24 CPU 96 CORE,2000步计算时间都不超... 相似文献
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两相流的六方程模型是双曲非守恒型系统,并具有非平衡源项.基于密度的方程求解方法则包含了齐次的双曲型方程求解以及非平衡源项的松弛过程.在齐次方程的求解中,Godunov型格式下的时间步长受到CFL数小于1的限制,计算效率不高.显式大时间步(LTS)格式是双曲守恒型方程的求解中突破CFL数限制的重要方法之一.在线性波的假设下,本文将通量差分裂(FDS)形式的LTS格式推广到了非守恒型的两相流六方程模型的求解中,提出了基于HLLC型Riemann求解器的LTS格式(LTS-HLLC).研究表明,在两相明显分离的区域,LTS-HLLC格式下增大CFL数可以减小数值粘性,提升了对激波等间断的分辨率也更易产生振荡,这与双曲守恒型方程中LTS格式的效果相同.但是在两相混合的区域,增大CFL数会加大松弛过程的耗散,使得对间断的分辨率反而降低.采用LTS-HLLC格式提高CFL数可以有效降低计算消耗的CPU时间,提高计算效率. 相似文献
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讨论了抛物化NS方程(parabolized Navier-Stokesequations, PNS)的数学性质,对比分析多种处理流向压力梯度的方法的优缺点. 以此为基础,成功地将LU-SGS隐式时间积分方法推广到PNS方程的流向空间积分上,发展了基于PNS方程的有限体积单次扫描空间推进算法(single-sweep parabolized Navier-Stokesalgorithm, SSPNS). 在该算法中,横向无黏数值通量和黏性通量分别采用混合型迎风格式和中心格式求解. 用SSPNS算法计算了4个典型流场,包括超声速平板流、15$^circ$楔板压缩高超声速流、带攻角的高超声速锥形流和侧压式高超声速进气道流动. SSPNS计算结果与NASA UPS程序数值结果、文献提供的实验数据及理论分析结果符合得很好.对比研究表明,SSPNS 法与传统时间迭代法相比,二者计算精度相当,而SSPNS计算速度快1~2个量级,存储量至少低1个量级.关键词 抛物化NS方程;空间推进算法;LU-SGS隐式积分方法;超声速/高超声速流动 相似文献
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The positivity-preserving scheme for the flux reconstruction (FR) framework is studied in this paper. A simple and direct implementation of the scheme is also proposed. Owing to the scheme and the implementation, FR or other high-order nodal methods can provide completely physically meaningful solutions at each time step. Their robustness is greatly enhanced. In the numerical tests, the solving of Euler equations coupled with artificial viscosity and Navier–Stokes equations is focused. Satisfying results are obtained in problems that include strong shocks or vacuum states. 相似文献
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J. Peradze 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(12):993-1001
A boundary value problem of Timoshenko plate equilibrium in axially symmetric displacements is considered. From the given system of ordinary differential equations an integro‐differential equation is singled‐out with respect to the plate deflection w that, together with the Dirichlet boundary conditions, makes up a boundary value problem. After finding w, other plate displacement characteristics u and ψ are defined. To approximate the problem solution for w, the Galerkin method is used. It leads to a nonlinear system of algebraic equations that is solved by the iteration method. The convergence of the iteration process is established and the error estimates are obtained for the displacement characteristics under some natural conditions. All constants from these conditions and the inequalities for the error are expressed explicitly through the initial data of the problem. The numerical examples illustrating the convergence conditions are given. 相似文献
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A fully implicit high-order preconditioned flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier-Stokes equations at low Mach numbers. A dual-time stepping approach with the second-order backward differentiation formula (BDF2) is employed to ensure temporal accuracy for unsteady flow simulation. When dynamic meshes are used to handle moving/deforming domains, the geometric conservation law is implicitly enforced to eliminate errors due to the resolution discrepancy between BDF2 and the spatial FR/CPR discretization. The large linear system resulted from the spatial and temporal discretizations is tackled with the restarted generalized minimal residual solver in the PETSc (portable, extensible toolkit for scientific computation) library. Through several benchmark steady and unsteady numerical tests, the preconditioned FR/CPR methods have demonstrated good convergence and accuracy for simulating flows at low Mach numbers. The new flow solver is then used to study the effects of Mach number on unsteady force generation over a plunging airfoil when operating in low-Mach-number flows. It is observed that weak compressibility has a significant impact on thrust generation but has a negligible effect on lift generation of an oscillating airfoil. 相似文献
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Satya P. Jammy Gihan R. Mudalige Istvan Z. Reguly Neil D. Sandham Mike Giles 《International Journal of Computational Fluid Dynamics》2016,30(6):450-454
abstractIn this paper, we report the development and validation of a compressible solver with shock capturing, using a domain-specific high-level abstraction framework, OPS, that is being developed at the University of Oxford. OPS uses an active library approach for block-structured meshes, capable of generating codes for a variety of parallel implementations with different parallelisation strategies. Performance results on various architectures are reported for the 1D Shu–Osher test case. 相似文献
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针对无网格Galerkin法计算耗时的问题,采用逐节点对法来组装刚度矩阵、共轭梯度法求解基于CSR格式存储的稀疏线性方程组,提出了一种利用罚函数法施加本质边界条件的EFG法GPU加速并行算法,给出了刚度矩阵和惩罚刚度矩阵的统一格式,以及GPU加速并行算法的流程图。编写了基于CUDA构架平台的GPU程序,且在NVIDIA GeForce GTX 660显卡上通过数值算例对所提算法进行了性能测试与分析比较,探讨了影响加速比的因素。算例结果验证了所提算法的可行性,并在满足计算精度的前提下,其加速比最大可达17倍;同时线性方程组的求解对加速比起决定性影响。 相似文献
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模板选择方式对非结构有限体积方法的计算准确性会产生显著影响. 在之前的工作中, 基于局部方向模板存在的问题, 我们探索了一种更加简单有效的全局方向模板选择方法, 并将其应用于二阶精度非结构有限体积求解器. 基于该方法找到的模板单元均沿着壁面法向与流向, 可有效捕捉流场变化, 反映流动的各向异性, 并且模板选择过程脱离了对网格拓扑的依赖, 避免了局部方向模板选择方法中复杂的阵面推进与方向判断过程, 克服了在大压缩比三角形网格上模板单元偏离壁面法向的现象, 同时在二阶精度求解器上得到了较高的计算精度与计算准确性. 为了进一步验证全局方向模板在高阶精度非结构有限体积方法中应用的可行性, 本文初步测试了该模板对变量梯度及高阶导数重构的影响. 经检验, 在不同类型的网格上, 采用全局方向模板得到的变量梯度与高阶导数误差明显低于局部方向模板, 同时也低于共点模板的计算误差. 此外, 在高斯积分点处由全局方向模板得到的变量点值与导数误差同样在三种模板中最低. 因此该模板选择方法在非结构有限体积梯度与高阶导数重构方面具有较好的数值表现, 具备在高阶精度非结构有限体积求解器中应用并推广的可行性. 相似文献
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Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M ≈0.1, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high-performance DG solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node-level performance, and our results suggest that there is great potential for further performance improvements for current state-of-the-art DG implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one. 相似文献
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三维大规模有限差分网格生成技术是三维有限差分计算的基础,网格生成效率是三维有限差分网格生成的研究热点。传统的阶梯型有限差分网格生成方法主要有射线穿透法和切片法。本文在传统串行射线穿透法的基础上,提出了基于GPU （graphic processing unit）并行计算技术的并行阶梯型有限差分网格生成算法。并行算法应用基于分批次的数据传输策略,使得算法能够处理的数据规模不依赖于GPU内存大小,平衡了数据传输效率和网格生成规模之间的关系。为了减少数据传输量,本文提出的并行算法可以在GPU线程内部相互独立的生成射线起点坐标,进一步提高了并行算法的执行效率和并行化程度。通过数值试验的对比可以看出,并行算法的执行效率远远高于传统射线穿透法。最后,通过有限差分计算实例可以证实并行算法能够满足复杂模型大规模数值模拟的需求。
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