CAJ | 학술논문

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。
제이、삼류변계조건대무망격대칭입자법구해순태열전도문제적계산정도화은정성유중요영향。제출일충유효적방법래처리저량류변계조건。해방법채용통일표체식묘술량류변계조건，병장변계입자분위광활역내적변계입자화비광활역적변계입자。대우전자，재온도도수적대칭입자근사중인입변계조건방정，정학지시가변계조건；대우후자，근거기상린입자적온도도수，채용구유일계련속성적입자근사，계산출기온도도수。응용해방법계산료일개수치산례。계산결과여해석해화유한원법적계산결과부합량호，차계산오차수시간정하강추세，설명해방법구유량호적정도화은정성。
Boundary conditions of the second and the third kind have important effects on the accuracy and stabili-ty of meshless symmetric particle method for the solution of transient heat conduction. An effective method is pre-sented 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 consid-ering 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 calculat-ed by a numerical example are in good agreement with analytical solutions and results obtained from the finite ele-ment method, which proves that the proposed method is accurate and stable.