本文選題：SPH核近似方法 + FODF-SPH方法　； 參考：《數(shù)學(xué)的實(shí)踐與認(rèn)識(shí)》2016年13期

【摘要】：在光滑粒子流體動(dòng)力學(xué)(Smooth Particle Hydrodynamics:SPH)核近似方法原理的基礎(chǔ)上,通過(guò)泰勒級(jí)數(shù)展開提出了計(jì)算函數(shù)導(dǎo)數(shù)的新FODF-SPH(Frist Order Derivative Free:FODF)方法,并分別推導(dǎo)一維、二維及三維情況下,計(jì)算函數(shù)的導(dǎo)數(shù)核估計(jì)的離散形式.用不同的粒子間距和不同的光滑長(zhǎng)度計(jì)算一維和二維函數(shù)導(dǎo)數(shù),與傳統(tǒng)SPH方法進(jìn)行誤差對(duì)比分析.結(jié)果表明,與傳統(tǒng)方法對(duì)比提出的計(jì)算方法的誤差小、收斂速度快且計(jì)算過(guò)程避免核函數(shù)導(dǎo)數(shù)計(jì)算等優(yōu)越性,因此在工程應(yīng)用和數(shù)值計(jì)算中具有較強(qiáng)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(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(51565054,51075346)
【分類號(hào)】：O35
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本文編號(hào)：1971193