共查询到12条相似文献，搜索用时 46 毫秒
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This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high‐order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier–Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity–velocity formulation for a two‐dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high‐order compact and non‐compact finite‐differences from fourth‐order to sixth‐order of accuracy. The other scheme used spectral methods instead of finite‐difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed‐order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics.This paper analyzes the accuracy of the immersed boundary method.The procedure contains two parts,i.e.,the code verification and the accuracy analysis.The code verification provides the confidence that the code used is free of mistakes,and the accuracy analysis gives the order of accuracy of the immersed boundary method.The method of manufactured solutions is taken as a means for both parts.In the first part,the numerical code employs a second-order discretization scheme,i.e.,it has second-order accuracy in theory.It matches the calculated order of accuracy obtained in the numerical calculation for all variables.This means that the code contains no mistake,which is a premise of the subsequent work.The second part introduces a jump in the manufactured solution for the pressure and adds the corresponding singular forcing terms in the momentum equations.By analyzing the discretization errors,the accuracy of the immersed boundary method is proven to be first order even though the discretization scheme is second order.It has been found that the coarser mesh may not be sensitive enough to capture the influence of the immersed boundary,and the refinement on the Lagrangian markers barely has any effect on the numerical calculation. 相似文献
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随着计算机技术的飞速进步,计算流体力学得到迅猛发展,数值计算虽能够快速得到离散结果,但是数值结果的正确性与精度则需要通过严谨的方法来进行验证和确认.制造解方法和网格收敛性研究作为验证与确认的重要手段已经广泛应用于计算流体力学代码验证、精度分析、边界条件验证等方面.本文在实现标量制造解和分量制造解方法的基础上,通过将制造解方法精度测试结果与经典精确解(二维无黏等熵涡)精度测试结果进行对比,进一步证实了制造解精度测试方法的有效性,并将两种制造解方法应用于非结构网格二阶精度有限体积离散格式的精度测试与验证,对各种常用的梯度重构方法、对流通量格式、扩散通量格式进行了网格收敛性精度测试.结果显示,基于Green-Gauss公式的梯度重构方法在不规则网格上会出现精度降阶的情况,导致流动模拟精度严重下降,而基于最小二乘(least squares)的梯度重构方法对网格是否规则并不敏感.对流通量格式的精度测试显示,所测试的各种对流通量格式均能达到二阶精度,且各方法精度几乎相同;而扩散通量离散中界面梯度求解方法的选择对流动模拟精度有显著影响. 相似文献
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Using a barotropic semi-geostrophic model with topographic forcing the stability and solutions of the nonlinear Rossby waves are discussed. It is found that the effects of the W-E oriented topography and the N-S oriented topography on the stability and phase speed of the waves are quite different. It is also found that the nonlinear Rossby waves forced by the topography can be described by the well-known KdV equation. 相似文献
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C. O. E. Burg V. K. Murali 《International Journal of Computational Fluid Dynamics》2013,27(7):521-532
The method of manufactured solutions (MMS) is a solution verification methodology for determining whether the implementation of a discretization method is achieving its theoretical order of accuracy. This methodology combines the advantages of grid refinement studies and comparison with exact solution, by modifying the governing equations solved within a code by adding a source term to drive the solution towards a predetermined analytic function. By solving the modified equations on a sequence of grids and comparing the differences between the converged solution and manufactured solution, the order of accuracy of the implementation can be investigated. However, in its current form, converged solutions on a sequence of grids are required which can be quite costly and difficult to obtain. In this paper, by comparing the MMS to the method for determining the theoretical order of accuracy of a discretization method, the residual formulation of the MMS is developed. This new formulation only requires that the residual of the discretized governing equations to be calculated and not the solution to the discretized equations, thus avoiding the computational cost and difficulties inherent in obtaining converged solutions. Furthermore, since only the residuals are interrogated, individual components of the flow solver can be tested, in isolation, allowing the MMS to be used more effectively in locating errors within the code. This new approach is demonstrated to yield the same order of accuracy as the original MMS using three different cases—one-dimensional porous media equation, one-dimensional St Venant equations and two-dimensional unstructured Navier–Stokes simulations. 相似文献
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The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes. The Premo code employs a node‐centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second‐order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度. 相似文献
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计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度. 相似文献
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Yuanping He Zhaolin Gu Junwei Su Chungang Chen Mingxu Zhang Liyuan Zhang Weizhen Lu 《国际流体数值方法杂志》2018,88(3):117-140
In this paper, we present a new numerical scheme to describe the dynamic evolution of multiphase polydisperse systems in terms of time, space, and properties by coupling the Eulerian‐Lagrangian method for air‐particle two‐phase flow and population balance equations to describe particle property evolution due to microbehaviors (eg, aggregation, breakage, and growth). This coupling scheme was used to comprehensively simulate the two‐phase flow structure, particle size spectrum, particle number, and volume concentrations. These were characterized by a high‐resolution particle tracking using the Lagrangian approach and the high precision of moments of the particle size spectrum by solving the population balance equation with the quadrature method of moments. The algorithm of the coupling scheme was incorporated into the open source computational fluid dynamics software OpenFOAM to simulate the dynamic evolution of vehicle exhaust plume. The impacts of vehicle velocity, exhaust temperature, and aggregation efficiency on the distribution of auto exhaust particles in space and changes in their properties were analyzed. The results indicate that the particle number concentration, volume concentration, and average diameter of particles in the vehicle exhaust plume could be strongly affected by the plume structure and flow properties. 相似文献
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Based on the body-fitted coordinate (BFC) method, a three-dimensional finite difference computer code, BFC3DGW, was developed to simulate groundwater flow problems. Methodology and solution procedures of the BFC method for simulating groundwater flows, particularly when the flow domain is stationary as in the case of confined aquifers, are described. The code was verified by comparing numerical results with analytical solutions for well-flow problems in an isosceles right-triangular aquifer. An example simulation is made to demonstrate capability of the code for solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. The method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation, the simplified implementation of boundary conditions, and the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape. 相似文献