温度场有限容积法程序入门之三：2D温度场显式迭代计算（暂不考虑

????????? 我们首先介绍温度场的求解吧，假设边界条件和初始条件已经设定。在贴代码之前，我们先谈谈这个类需要什么属性和行为：节点数组用于存储计算变量、网格大小、维度定义、计算函数，也就这么多了。如何计算某节点的温度？计算其东南西北方位相接节点对该节点的穿导热之和即可，读者这里可以考虑一下如何添加源相和对流换热进去。

package Soong.Solver
{
	public class TSolver
	{
		public  var Tlist:Vector.<Node>;
		
		private var xGridNum:uint = 1;//Number of Grid Allocated in X Direction
		private var yGridNum:uint = 1;//Number of Grid Allocated in X Direction
		
		public var dx:Number = 1;//Grid Size in X Direction
		public var dy:Number = 1;//Grid Size in Y Direction
		
		public var Sx:Number = 0;//Area of Heat Interface in X Direction
		public var Sy:Number = 0;//Area of Heat Interface in X Direction
		
		public var cellVol:Number = 0;//Volume of Control Volume
		
		public var Freezing:Boolean=false;//If Time to Freeze
		
		public function TSolver(xGridNum:uint,yGridNum:uint,dx:Number,dy:Number)
		{
			this.xGridNum = xGridNum;
			this.yGridNum = yGridNum;
			
			this.dx = dx;
			this.dy = dy;
			
			this.Sx = dy * 1;
			this.Sy = dx * 1;
			
			this.cellVol = dx * dy * 1;
		}
		
		public function Step(timeStep:Number):void
		{
			var col:uint = 0;
			var row:uint = 0;
			var node:Node = null;
			
			for (col = 2; col < xGridNum - 2; col++ )
			{
				for (row = 2; row < yGridNum-2; row++ )
				{
					node = Tlist[Index(col,row)] as Node;
					
					CalTnext(timeStep,node,col,row);
					
					node.T0=node.T;
				}
			}
		}
		
		public function CalTnext(timeStep:Number,node:Node,col:uint,row:uint):void
		{
			var conner:Boolean=false;
			var node_Adj:Node = null;
			
			var conductionHeat:Number = 0;
			
			//For Node on/in Connor or Edge
			var SxFix:Number=1;//Area Fix Factor For Non-Interior Region in X Direction
			var SyFix:Number=1;//Area Fix Factor For Non-Interior Region in Y Direction
			
			var VolFix:Number=1;//Volume Fix Factor For Non-Interior Region in Y Direction
			
			if(((col==2)&&(row==2))||((col==2)&&(row==yGridNum-3))||((col==xGridNum-3)&&(row==2))||((col==xGridNum-3)&&(row==yGridNum-3)))
			{
				SxFix=1/2.0;
				SyFix=1/2.0;
				
				conner=true;
			}
			
			if((col==2)||(col==xGridNum-3))
			{
				VolFix/=2;
				
				if(!conner)
				{
					SyFix=1/2.0;
				}
			}
			
			if((row==2)||(row==yGridNum-3))
			{			
				VolFix/=2;
				
				if(!conner)
				{
					SxFix=1/2.0;
				}
			}
			
			node_Adj = Tlist[Index(col+1,row)] as Node;
			conductionHeat+=node.eHeatExchangeFactor*(node_Adj.T0-node.T0)*Sx*SxFix;
			
			node_Adj = Tlist[Index(col-1,row)] as Node;
			conductionHeat+=node.wHeatExchangeFactor*(node_Adj.T0-node.T0)*Sx*SxFix;
			
			node_Adj = Tlist[Index(col,row+1)] as Node;
			conductionHeat+=node.nHeatExchangeFactor*(node_Adj.T0-node.T0)*Sy*SyFix;
			
			node_Adj = Tlist[Index(col,row - 1)] as Node;
			conductionHeat+=node.sHeatExchangeFactor*(node_Adj.T0-node.T0)*Sy*SyFix;
			
			var dT:Number = conductionHeat * timeStep;
			dT /= cellVol * VolFix * node.Rho * node.Cp;
			
			node.T = node.T0 + dT;
		}
		
		public function LatentHeatRelease(node:Node):void
		{
			
		}
		
		//Apply the Boundary Condition
		public function ApplyBC():void
		{
			
		}
		
		private function Index(col:uint=0,row:uint=0):uint
		{
			return row * xGridNum + col;
		}
	}
}

??????? 简单吧，需要注意的是不同位置的节点其传热面积以及控制体体积不尽相同，需要Fix一下。可以预见，如果将SxFix、SyFix，VolFix设置为Node类的成员变量，计算会更快。这里给出初步的计算结果（迭代100s的结果）。目前笔者没有贴出所有代码，这时按照笔者提供的程序是无法运行的，读者想想，还缺点什么？

????? 将其对称得到整个界面：

??? 有点样子了，这还不是最终的计算结果，凝固潜热还没有考虑进去，可以使用物理意义明确的温度回升法处理。另外，我们没有离散偏微分方程，但是我们的方法和离散偏微分方程殊途同归的。也许读者可以理解有限差分和有限容积的连续与区别了。