Numerical solution of compressible flow in a channel and blade cascade

This paper deals with a numerical solution of compressible flows. In the case of Euler equations, a numerical solver is presented on a structured quadrilateral grid. The Advection Upstream Splitting Method (AUSM) scheme is used and the spatial accuracy is improved by linear reconstruction with slope limiters. The influence of those limiters are then tested in cases of transonic flow through a channel and a blade cascade.     

Analysis of newton multilevel stabilized finite volume method for the three‐dimensional stationary Navier‐Stokes equations

This article proposes and analyzes a multilevel stabilized finite volume method(FVM) for the three‐dimensional stationary Navier–Stokes equations approximated by the lowest equal‐order finite element pairs. The method combines the new stabilized FVM with the multilevel discretization under the assumption of the uniqueness condition. The multilevel stabilized FVM consists of solving the nonlinear problem on the coarsest mesh and then performs one Newton correction step on each subsequent mesh thus only solving one large linear systems. The error analysis shows that the multilevel‐stabilized FVM provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the stationary Navier–Stokes equations on a fine mesh for an appropriate choice of mesh widths: h_j ～ h_j‐1², j = 1,…,J. Therefore, the multilevel stabilized FVM is more efficient than the standard one‐level‐stabilized FVM. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Numeric treatment of contact discontinuity with multi-gases

In this paper we work with a finite-volume-procedure for the computation of the one-dimensional Euler equations for the treatment of multi-gases and the problem of the correct treatment of the discontinuity was more nearly investigated. A suggested equation was embedded in the finite volumes context and implemented in our code accordingly and regarded as validated.     

Thermal analysis of high-index-contrast grating (HCG)-based VCSEL

A 3-D thermal analysis of 870 nm high-index-contrast grating (HCG)-based vertical cavity surface emitting laser (VCSEL) by using finite volume method (FVM) is presented in this paper. The HCG-based VCSEL is modeled by applying a steady-state 3-D heat dissipation model. Temperature distribution profile and thermal resistance (R_th) of the device are investigated by inserting the heat source value into the thermal simulation. Also, this analysis is performed for a conventional VCSEL operating at the same wavelength and under the same injected current as well as the same geometric sizes. The analysis shows that the maximum temperature inside the HCG-based VCSEL is lower than that inside the conventional VCSEL.     

求解可压缩流的高精度非结构网格WENO有限体积法

提出-种基于最小二乘重构和WENO限制器的非结构网格高精度有限体积方法.用中心网格的某些邻居网格建立重构多项式,给出-定的原则搜索和存储足够多的邻居网格以建立重构多项式,采用最小二乘法求解重构多项式的系数.用-种通用的方法控制重构邻居个数,以减少存储和计算,采用WENO限制器和旋转Riemann求解器以达到统-的高精度并且抑制守恒律方程求解中的非物理振荡.为检验上述算法,以基于节点的梯度重构,Bath and Jesperson限制器的二阶算法为基准,给出三阶和四阶格式与二阶格式以及高阶格式若干经典算例计算结果的对比和分析.     

An adaptive gradient smoothing method (GSM) for fluid dynamics problems

In this paper, a novel adaptive gradient smoothing method (GSM) based on irregular cells and strong form of governing equations for fluid dynamics problems with arbitrary geometrical boundaries is presented. The spatial derivatives at a location of interest are consistently approximated by integrally averaging of gradients over a smoothing domain constructed around the location. Such a favorable GSM scheme corresponds to a compact stencil with positive coefficients of influence on regular cells. The error equidistribution strategy is adopted in the solution‐based adaptive GSM procedure, and adaptive grids are attained with the remeshing techniques and the advancing front method. In this paper, the adaptive GSM has been tested for solutions to both Poisson and Euler equations. The sensitivity of the GSM to the irregularity of the grid is examined in the solutions to the Poisson equation. We also investigate the effects of error indicators based on the first derivatives and second derivatives of density, respectively, to the solutions to the shock flow over the NACA0012 airfoil. The adaptive GSM effectively yields much more accurate results than the non‐adaptive GSM solver. The whole adaptive process is very stable and no spurious behaviors are observed in all testing cases. The cosmetic techniques for improving grid quality can effectively boost the accuracy of GSM solutions. It is also found that the adaptive GSM procedure using the second derivatives of density to estimate the error indicators can automatically and accurately resolve all key features occurring in the flow with discontinuities. Copyright © 2009 John Wiley & Sons, Ltd.     

Formulation and testing of the FTn finite volume method for radiation in 3-D complex inhomogeneous participating media

In the present study, an original three-dimensional formulation of the FTn finite volume method based on the bounded high-resolution CLAM schema and using the blocked-off-region technique has been developed. Firstly, this model is applied for 3D inhomogeneous L-shaped absorbing/emitting and isotropically scattering media. Both isothermal medium and medium with internal uniform and non-uniform volumetric heat generation are considered. Secondly, the present FTn FVM results for 3D combustion chamber with five baffles are illustrated and discussed. All tests bring to the fore the advantages, in 3D problems, of the FTn FVM comparatively with the standard FVM especially for inhomogeneous media with discontinuous volumetric heat sources. However these benefits still quantitative and no qualitative discrepancy between the FTn FVM and the popular FVM results are registered.     

风沙流对高压绝缘子电位和电场分布的影响

研究风沙流对高压绝缘子电位和电场分布的影响,基于有限体积法建立绝缘子风沙气固两相流模型和风沙天气下绝缘子的风-沙-电耦合场模型,计算不同风沙天气下绝缘子表面沙尘的空间分布和沉积及其对绝缘子沿面电位和电场的影响,结果表明：风沙天气下绝缘子沿面电位和电场畸变受风速和粒径影响显著,电位的畸变幅度随风速和粒径的增加而升高,电场的畸变幅度随风速和粒径的增大而减少;风沙天气下绝缘子表面不同的沙尘空间分布和沉积导致绝缘子不同位置沿面电位和电场畸变不同.     

A new r‐ratio formulation for TVD schemes for vertex‐centered FVM on an unstructured mesh

The r‐ratio is a parameter that measures the local monotonicity, by which a number of high‐resolution and TVD schemes can be formed. A number of r‐ratio formulations for TVD schemes have been presented over the last few decades to solve the transport equation in shallow waters based on the finite volume method (FVM). However, unlike structured meshes, the coordinate directions are not clearly defined on an unstructured mesh; therefore, some r‐ratio formulations have been established by approximating the solute concentration at virtual nodes, which may be estimated from different assumptions. However, some formulations may introduce either oscillation or diffusion behavior within the vertex‐centered (VC) framework. In this paper, a new r‐ratio formulation, applied to an unstructured grid in the VC framework, is proposed and compared with the traditional r‐ratio formulations. Through seven commonly used benchmark tests, it is shown that the newly proposed r‐ratio formulation obtains better results than the traditional ones with less numerical diffusion and spurious oscillation. Moreover, three commonly used TVD schemes—SUPERBEE, MINMOD, and MUSCL—and two high‐order schemes—SOU and QUICK—are implemented and compared using the new r‐ratio formulation. The new r‐ratio formulation is shown to be sufficiently comprehensive to permit the general implementation of a high‐resolution scheme within the VC framework. Finally, the sensitivity test for different grid types demonstrates the good adaptability of this new r‐ratio formulation. Copyright © 2015 John Wiley & Sons, Ltd.