Optimized meshfree methods for acoustics

When the Helmholtz equation is solved by numerical methods as, e.g., the finite element method (FEM), the solution suffers from the so-called pollution effect. The pollution is mainly caused by the dispersion, meaning that the numerical wave number disagrees with the wave number of the exact solution. This leads to inaccurate results, especially for high wave numbers. In order to obtain acceptable results also for higher wave numbers, either a high element resolution or elements of a higher order can be used. For either option the consequence is an increased computation time and memory capacity.Meshfree methods as the element free Galerkin method (EFGM) and the radial point interpolation method (RPIM) are not dispersion-free either, but it has been shown that meshfree methods are able to reduce the dispersion significantly. Both methods offer several parameters, which can be modified in order to obtain optimal results with respect to the dispersion effect. This work presents an exhaustive parameter study on both the EFGM and the RPIM. It is shown, that the methods can be significantly improved if certain parameters as, e.g., weighting functions, shape parameters, size of the influence domain, are chosen appropriately.     

Second law analysis of momentum and heat transfer in unit operations

Momentum and heat transfer in complex systems always is the sum of single and simple transfer elements here called unit operations. They are usually characterised by head loss coefficients and Nusselt numbers as far as the flow and the heat transfer aspect is concerned. In our study we show that this is insufficient for a complete assessment and that additional parameters should be introduced. They take into account that energy, its use and conversion always is subject to the constraints set by the second law of thermodynamics.     

粗糙壁面通道内的流动研究

通过对流动中熵产的数值计算,研究了管道和平面通道内流动中粗糙壁面对摩擦的影响.研究表明,在层流流动中壁面粗糙度的影响也是值得重视的,尽管这种效应以往常常被人们所忽视.除了可得到摩擦因子之外,由于可以得知流场中壁面粗糙单元附近的耗散分布,因此可深入理解这一物理现象的本质.为了对粗糙壁面通道内的流动进行简明的描述,需要对壁面位置和粗糙度参数进行合理的选择,并对各种选择方案进行了讨论和评价.     

Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation

When numerical methods such as the finite element method (FEM) are used to solve the Helmholtz equation, the solutions suffer from the so‐called pollution effect which leads to inaccurate results, especially for high wave numbers. The main reason for this is that the wave number of the numerical solution disagrees with the wave number of the exact solution, which is known as dispersion. In order to obtain admissible results a very high element resolution is necessary and increased computational time and memory capacity are the consequences. In this paper a meshfree method, namely the radial point interpolation method (RPIM), is investigated with respect to the pollution effect in the 2D‐case. It is shown that this methodology is able to reduce the dispersion significantly. Two modifications of the RPIM, namely one with polynomial reproduction and another one with a problem‐dependent sine/cosine basis, are also described and tested. Numerical experiments are carried out to demonstrate the advantages of the method compared with the FEM. For identical discretizations, the RPIM yields considerably better results than the FEM. Copyright © 2008 John Wiley & Sons, Ltd.