發(fā)布時間：2018-06-03 02:56

  本文選題：SPH核近似方法 + FODF-SPH方法��； 參考：《數(shù)學的實踐與認識》2016年13期

【摘要】：在光滑粒子流體動力學(Smooth Particle Hydrodynamics:SPH)核近似方法原理的基礎上,通過泰勒級數(shù)展開提出了計算函數(shù)導數(shù)的新FODF-SPH(Frist Order Derivative Free:FODF)方法,并分別推導一維、二維及三維情況下,計算函數(shù)的導數(shù)核估計的離散形式.用不同的粒子間距和不同的光滑長度計算一維和二維函數(shù)導數(shù),與傳統(tǒng)SPH方法進行誤差對比分析.結果表明,與傳統(tǒng)方法對比提出的計算方法的誤差小、收斂速度快且計算過程避免核函數(shù)導數(shù)計算等優(yōu)越性,因此在工程應用和數(shù)值計算中具有較強的適用范圍.
[Abstract]:Based on the principle of smooth particle hydrodynamics and the kernel approximation method of smooth Particle hydrodynamics, a new FODF-SPH(Frist Order Derivative free: FODF method for calculating the derivative of function is proposed by Taylor series expansion, and the one-dimensional, two-dimensional and three-dimensional cases are derived, respectively. The discrete form of the derivative kernel estimation of a function is calculated. The derivatives of one-dimensional and two-dimensional functions are calculated by using different particle spacing and different smooth length, and the error is compared with the traditional SPH method. The results show that compared with the traditional method, the proposed method has the advantages of small error, fast convergence and avoiding the calculation of the derivative of kernel function, so it has a strong scope of application in engineering application and numerical calculation.
【作者單位】： 新疆大學數(shù)學與系統(tǒng)科學學院;
【基金】：國家自然科學基金(51565054,51075346)
【分類號】：O35
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本文編號：1971193