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称为外部力，一般就是重力"))]),Q("mjx-container",L,[(t(),a("svg",Z,T[17]||(T[17]=[m('',1)]))),T[18]||(T[18]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true"},[Q("mlabeledtr",null,[Q("mtd",null,[Q("mtext",null,"(2.4)")]),Q("mtd",null,[Q("msup",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mover",null,[Q("mi",null,"F"),Q("mo",{stretchy:"false"},"→")])]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"e"),Q("mi",null,"x"),Q("mi",null,"t"),Q("mi",null,"e"),Q("mi",null,"r"),Q("mi",null,"n"),Q("mi",null,"a"),Q("mi",null,"l")])]),Q("mo",null,"="),Q("mi",null,"ρ"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mover",null,[Q("mi",null,"g"),Q("mo",{stretchy:"false"},"→")])])])])])])],-1))]),Q("p",null,[Q("mjx-container",D,[(t(),a("svg",w,T[19]||(T[19]=[m('',1)]))),T[20]||(T[20]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msup",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mover",null,[Q("mi",null,"F"),Q("mo",{stretchy:"false"},"→")])]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"p"),Q("mi",null,"r"),Q("mi",null,"e"),Q("mi",null,"s"),Q("mi",null,"s"),Q("mi",null,"u"),Q("mi",null,"r"),Q("mi",null,"e")])])])],-1))]),T[21]||(T[21]=l("是由流体内部的压力差产生的作用力，试想一下在水管中流动的液体，进水口区域的压力一定会比出水口区域大，所以液体才会源源不断的流动，数值上，它等于压力场的梯度，方向由压力高的区域指向压力低的区域。"))]),Q("mjx-container",v,[(t(),a("svg",V,T[22]||(T[22]=[m('',1)]))),T[23]||(T[23]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true"},[Q("mlabeledtr",null,[Q("mtd",null,[Q("mtext",null,"(2.5)")]),Q("mtd",null,[Q("msup",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mover",null,[Q("mi",null,"F"),Q("mo",{stretchy:"false"},"→")])]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"p"),Q("mi",null,"r"),Q("mi",null,"e"),Q("mi",null,"s"),Q("mi",null,"s"),Q("mi",null,"u"),Q("mi",null,"r"),Q("mi",null,"e")])]),Q("mo",null,"="),Q("mo",null,"−"),Q("mi",{mathvariant:"normal"},"∇"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"p")])])])])])],-1))]),Q("p",null,[Q("mjx-container",j,[(t(),a("svg",b,T[24]||(T[24]=[m('',1)]))),T[25]||(T[25]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msup",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mover",null,[Q("mi",null,"F"),Q("mo",{stretchy:"false"},"→")])]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"v"),Q("mi",null,"i"),Q("mi",null,"s"),Q("mi",null,"c"),Q("mi",null,"o"),Q("mi",null,"s"),Q("mi",null,"i"),Q("mi",null,"t"),Q("mi",null,"y")])])])],-1))]),T[28]||(T[28]=l("是由粒子之间的速度差引起的，设想在流动的液体内部，快速流动的部分会施加类似于剪切力的作用力到速度慢的部分，这个力的大小跟流体的粘度系数")),Q("mjx-container",y,[(t(),a("svg",R,T[26]||(T[26]=[Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D707",d:"M58 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如果你学习过流体力学，一定会发现上面这个公式就是Navier-Stokes方程的一个简单形式，但N-S方程有更严格的形式和推导过程，感兴趣的朋友可以从流体力学相关的书中找到，这里有一篇比较比较浅显的文档可以参考，经过联系作者flysea，拿到这篇文档的原始文件放在这里，再次感谢flysea的帮助。
实际运算过程中，有时还要考虑表面张力的影响，所谓表面张力大家应该并不陌生，肥皂泡、毛细管等有趣的物理现象都跟表面张力有关，这个力可以简单理解为流体试图减小表面而产生的力。

由于表面张力只涉及到表层的粒子，所以计算方法和上面的有所不同，这部分会在以后的章节介绍。
经过上面的分析，我们基本上搞清楚了SPH粒子的运动计算方法，下节我们将正式开始介绍SPH算法的关键部分，如何通过光滑核函数计算粒子运动规律。

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