三维瞬态热传导问题的无网格对称粒子法

为了准确分析瞬态热传导问题,构造了一种三维无网格对称粒子法。首先,基于泰勒级数展开和加权最小二乘方法导出了一阶导数的对称粒子近似。然后,利用得到的粒子近似离散一阶导数,建立了求解三维瞬态热传导问题的无网格对称粒子法。应用该方法计算了各向同性介质中的瞬态热传导问题,得到了典型时刻的温度分布,计算结果与解析解吻合良好,验证了该方法的正确性。进一步将该方法应用于各向异性介质热传导和非线性热传导问题,计算结果与有限元法的计算结果非常接近,说明该方法对于复杂热传导问题的求解也是可行的。

Meshless Symmetric Particle Method for 3D Transient Heat Conduction

To accurately analyze transient heat conduction problems, a 3D Meshless Symmetric Particle Method (MSPM) is established. Firstly, a Symmetric Particle Approximation (SPM) having high accuracy is derived based on Taylor series expansion and weighted least squares method. Then, SPM is used to discretize the first order derivatives, and a meshless symmetric particle method (MSPM) for solving transient heat conduction problems is obtained. The MSPM is applied to solve heat conduction in a homogeneous media. The calculated temperature results are in good agreement with analytical results. This demonstrates the correctness of the method. The method is further used for analyzing heat conduction in orthotropic media and nonlinear heat conduction. Computed results of the method are found very close to those of Finite Element Method. This indicates the method is also feasible for complicated heat conduction problems.