无网格对称粒子法中两类热边界条件的处理

第二、三类边界条件对无网格对称粒子法求解瞬态热传导问题的计算精度和稳定性有重要影响。提出一种有效的方法来处理这两类边界条件。该方法采用统一表达式描述两类边界条件,并将边界粒子分为光滑域内的边界粒子和非光滑域的边界粒子。对于前者,在温度导数的对称粒子近似中引入边界条件方程,精确地施加边界条件;对于后者,根据其相邻粒子的温度导数,采用具有一阶连续性的粒子近似,计算出其温度导数。应用该方法计算了一个数值算例。计算结果与解析解和有限元法的计算结果符合良好,且计算误差随时间呈下降趋势,说明该方法具有良好的精度和稳定性。

Treatment of Two Kinds of Thermal Boundary Conditions in Meshless Symmetric Particle Method

Boundary conditions of the second and the third kind have important effects on the accuracy and stability of meshless symmetric particle method for the solution of transient heat conduction. An effective method is presented in this paper to treat boundary conditions of both kinds. Two kinds of boundary conditions are expressed in a uniform form, and boundary particles are divided into two categories, the particles in smooth boundary regions and particles in non-smooth boundary regions. For the former, boundary conditions are enforced exactly by considering the equations of boundary conditions as constraints in the symmetric particle approximation of derivatives of temperature. For the later, their derivatives of temperature are approximated with a particle approximation of first-order consistency based on the derivatives of temperature of neighboring particles. The numerical results calculated by a numerical example are in good agreement with analytical solutions and results obtained from the finite element method, which proves that the proposed method is accurate and stable.