本文關(guān)鍵詞： 格子玻爾茲曼模型 FitzHugh-Nagumo方程 Chapman-Enskog展開(kāi) 有限差分法　出處：《物理學(xué)報(bào)》2016年15期 　論文類型：期刊論文

【摘要】：格子玻爾茲曼方法在復(fù)雜的流體系統(tǒng)中得到了廣泛的應(yīng)用.本文針對(duì)在高于閾值常電流刺激下神經(jīng)元?jiǎng)幼麟娢恢芷谛哉袷幍腇itzHugh-Nagumo系統(tǒng),構(gòu)造了一類帶源項(xiàng)和修正項(xiàng)的仿真格子玻爾茲曼模型.通過(guò)合理選擇適當(dāng)?shù)木植科胶鈶B(tài)分布函數(shù)和修正函數(shù),再應(yīng)用Chapman-Enskog多尺度分析,可以正確恢復(fù)出一類宏觀非線性方程.通過(guò)積分法得到了修正函數(shù)的構(gòu)造方法,并分析了格子玻爾茲曼模型L~∞穩(wěn)定的充分條件.利用網(wǎng)格相關(guān)性分析,本文所構(gòu)造的模型具有二階空間精度.應(yīng)用本文所提出的模型,仿真模擬了幾個(gè)具有解析解的初邊值系統(tǒng),并與傳統(tǒng)的改進(jìn)有限差分格式(MFDM)進(jìn)行了對(duì)比,結(jié)果表明本文模型所得的數(shù)值解與解析解吻合,其模擬誤差小于MFDM.此外,還針對(duì)不具有解析解的初邊值系統(tǒng)進(jìn)行了數(shù)值仿真,并與MFDM進(jìn)行了對(duì)比.數(shù)值結(jié)果表明,兩種計(jì)算格式的數(shù)值解比較吻合,進(jìn)一步證明了本文所構(gòu)造模型的有效性和穩(wěn)定性.
[Abstract]:Lattice Boltzmann method has been widely used in complex fluid systems. This paper deals with the FitzHugh-Nagumo system of periodic oscillation of action potential of neurons under constant current stimulation above threshold. Tong. A kind of lattice Boltzmann model with source term and modified term is constructed, and the proper distribution function and correction function of local equilibrium state are reasonably selected. Using Chapman-Enskog multi-scale analysis, a class of macroscopic nonlinear equations can be recovered correctly, and the method of constructing the modified function is obtained by integral method. The sufficient conditions for the L鈭，

本文編號(hào)：1476646