温度场有限容积法程序入门之四：网格剖分.边界条件设置.迭代.导

首先给出代码：

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package Soong.Solver
{
	import flash.net.FileReference;
	public class TSolverMgr
	{
		public var xDim:Number = 20;//Dimension in X Direction
		public var yDim:Number = 20;//Dimension 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 IDsteel:uint = Math.pow(2,1);//ID of material Steel
		public var IDair:uint = Math.pow(2,2);//ID of material Air
		
		public var steel:Material = null;//Material Steel
		public var air:Material = null;//Material Air
		
		public var Tambient:Number = 30;//Temperature of Ambient Space (Eg: Air)
		public var ConvectionCoeff:Number = 100;//
		
		private var xGridNum:uint = 0;//Number of Grid Allocated in X Direction
		private var yGridNum:uint = 0;//Number of Grid Allocated in X Direction
		
		private var totalGridNum:uint = 0;//Total Number of Grid Allocated in 2D Plane
		
		private var keyGridNum:uint = 0;//Number of Key Grid
		
		private var xKeyGridNum:uint = 0;//Number of Key Grid in X Direction
		private var yKeyGridNum:uint = 0;//Number of Key Grid in Y Direction
		
		private var solver:TSolver = null;
		private var nodeList:Vector.<Node> = null;
		private var flowTime:Number=0;
		
		public function TSolverMgr()
		{
			
		}
		
		public function SetDim(xDim:Number=20,yDim:Number=20,dx:Number=1,dy:Number=1):void
		{
			this.xDim = xDim;
			this.yDim = yDim;
			
			this.dx = dx;
			this.dy = dy;
			
			xKeyGridNum = uint(xDim / dx) + 1;
			xGridNum = xKeyGridNum + 2 + 2;
			
			yKeyGridNum = uint(yDim / dy) + 1;
			yGridNum = yKeyGridNum + 2 + 2;
			
			totalGridNum = xGridNum * yGridNum;
			keyGridNum=xKeyGridNum*yKeyGridNum;
			
			solver = new TSolver(xGridNum,yGridNum,dx,dy);
			solver.Tlist = new Vector.<Node>(totalGridNum,true);
			
			nodeList = solver.Tlist;
			
			for(var i:uint=0;i<totalGridNum;i++)
			{
				nodeList[i]=new Node();
			}
		}
		
		public function ApplyMaterial(steel:Material,air:Material):void
		{
			this.steel = steel;
			
			this.air = air;
		}
		
		public function SetMaterial():void
		{
			steel = new Material(IDsteel,1550);
			
			steel.Cp = 680;
			steel.lmd = 34;
			steel.Rho = 7200;
			steel.LatentHeat = 270000;
			steel.Tsol = 1504;
			steel.Tliq = 1531;
			
			air = new Material(IDair,Tambient);
			air.Cp = 1008;
			air.lmd = 0.02;
			air.Rho = 1.29;
			air.LatentHeat = 0;
			
			var col:uint = 0;
			var row:uint = 0;
			var node:Node=null;
			
			//Apply the Steel Region
			for (col = 2; col < xGridNum - 2; col++ )
			{
				for (row = 2; row < yGridNum-2; row++ )
				{
					node = nodeList[Index(col,row)] as Node;
					
					node.ApplyMaterial(steel);
				}
			}
			
			//Apply the Upper Air Region 
			for (col = 0; col < xGridNum; col++ )
			{
				for (row = yGridNum-2; row < yGridNum; row++ )
				{
					node = nodeList[Index(col,row)] as Node;
					
					node.ApplyMaterial(air);
				}
			}
			
			//Apply the Right Air Region
			for (col = xGridNum - 2; col < xGridNum; col++ )
			{
				for (row = 0; row < yGridNum; row++ )
				{
					node = nodeList[Index(col,row)] as Node;
					
					node.ApplyMaterial(air);
				}
			}
		}
		
		public function UpdateHeatExchangeFactor():void
		{
			var col:uint = 0;
			var row:uint = 0;
			var xDir:Boolean = true;
			var node:Node = null;
			
			//Update Heat Exchange Factor in Steel Region
			for (col = 2; col < xGridNum - 2; col++ )
			{
				for (row = 2; row < yGridNum-2; row++ )
				{
					var node_Adj:Node=null;
					
					node = nodeList[Index(col,row)] as Node;
					
					node_Adj=nodeList[Index(col+1,row)] as Node;
					node.eHeatExchangeFactor = HeatExchangeFactor(node.materialIndex,node_Adj.materialIndex,true);
					
					node_Adj=nodeList[Index(col-1,row)] as Node;
					node.wHeatExchangeFactor = HeatExchangeFactor(node.materialIndex,true);
					
					node_Adj=nodeList[Index(col,row+1)] as Node;
					node.nHeatExchangeFactor = HeatExchangeFactor(node.materialIndex,false);
					
					node_Adj=nodeList[Index(col,row-1)] as Node;
					node.sHeatExchangeFactor = HeatExchangeFactor(node.materialIndex,false);
				}
			}
		}
		
		public function HeatExchangeFactor(mtlA:uint,mtlB:uint,xDir:Boolean=true):Number
		{
			 /* Interface Index
			  * 1 for Insulation,2 for Steel,4 For Air
			  * AB 1 2 4
			  * ----------
			  * 1| 2 3 5
			  * 2| 3 4 6
			  * 4| 5 6 8
			  */
			var interfaceAB:uint = mtlA + mtlB;
			
			var gridSize:Number = xDir?dx:dy;
			
			switch (interfaceAB)
			{
				case Material.HeatInsulation*2://Interface Between Insulation: 2
					return 0;
					break;
					
				case Material.HeatInsulation+steel.ID://Interface Between Insulation and Steel: 3
					return 0;
					break;
					
				case steel.ID*2://Interface Between Steel: 4
					return steel.lmd / gridSize;
					break;
					
				case Material.HeatInsulation+air.ID://Interface Between Insulation and Air: 5
					return 0
					break;
					
				case steel.ID+air.ID://Interface Between Steel and Air: 6
					return ConvectionCoeff;
					break;
					
				case air.ID*2://Interface Between Air: 8
					return air.lmd / gridSize;
					break;
				
				default:
					break;
			}
			
			return 0;
		}
		
		public function Step(timeStep:Number):void
		{
			flowTime+=timeStep;
			
			solver.Step(timeStep);
		}
		
		public function Export2Tecplot(fileName:String="Tdata.dat",precision:uint=5):void
		{
			var file:FileReference = new FileReference();
			
			var exData:String = new String("Title="Data Simulated By SoongSoftStudio"n");
			
			exData+="Variables="X","Y","T","Liquid Fraction"n";
			
			exData+="Zone T="Billet" I="+xKeyGridNum+",J="+yKeyGridNum+",K=1n";
			
			exData+="SOLUTIONTIME="+flowTime.toFixed(precision)+"n";
			
			var col:uint = 0;
			var row:uint = 0;
			
			var Tsol:Number=steel.Tsol;
			var dT:Number=steel.Tliq-Tsol;
			
			//Update Heat Exchange Factor in Steel Region
			for (col = 2; col < xGridNum - 2; col++ )
			{
				for (row = 2; row < yGridNum-2; row++ )
				{
					var x:Number=(col-2)*dx;
					var y:Number=(row-2)*dy;
					
					var T:Number=nodeList[Index(col,row)].T;
					var lf:Number=(T-Tsol)/dT;
					
					if (lf>1) lf=1;
					if(lf<0) lf=0;
					
					exData+=x.toFixed(precision)+" "+y.toFixed(precision)+" "+T.toFixed(precision)+" "+lf.toFixed(precision)+"n";
				}
			}
			
			file.save(exData,fileName);
		}
		
		public function GetCurrentT():Vector.<Number>
		{
			var result:Vector.<Number>=new Vector.<Number>();
			
			var col:uint = 0;
			var row:uint = 0;
			
			//Update Heat Exchange Factor in Steel Region
			for (col = 2; col < xGridNum - 2; col++ )
			{
				for (row = 2; row < yGridNum-2; row++ )
				{
					var T:Number=nodeList[Index(col,row)].T;
					
					result.push(T);
				}
			}
			
			return result;
		}
		
		private function Index(col:uint=0,row:uint=0):uint
		{
			return row * xGridNum + col;
		}
		
		public function ExportSetting(fileName:String="Setting.ini",precision:uint=1):void
		{
			var file:FileReference = new FileReference();
			
			var exData:String = new String("Title="Data Simulated By SoongSoftStudio"n");
			
			exData+="Variables="X","e","s","w","n"n";
			
			exData+="Zone T="Billet" I="+xGridNum+",J="+yGridNum+",K=1n";
			
			exData+="SOLUTIONTIME="+flowTime.toFixed(precision)+"n";
			
			var col:uint = 0;
			var row:uint = 0;
			
			var Tsol:Number=steel.Tsol;
			var dT:Number=steel.Tliq-Tsol;
			
			//Update Heat Exchange Factor in Steel Region
			for (col = 0; col < xGridNum ; col++ )
			{
				for (row = 0; row < yGridNum; row++ )
				{
					var idx:uint=Index(col,row);
					
					var x:Number=col*dx;
					var y:Number=row*dy;
					
					var node:Node=nodeList[idx];
					
					var Tini:Number=node.T0;

					var eHEF:Number=node.eHeatExchangeFactor;
					var sHEF:Number=node.sHeatExchangeFactor;
					var wHEF:Number=node.wHeatExchangeFactor;
					var nHEF:Number=node.nHeatExchangeFactor;
					
					exData+=x.toFixed(precision)+" "+y.toFixed(precision)+" "+Tini.toFixed(precision)+" "+eHEF.toFixed(precision)+" "+sHEF.toFixed(precision)+" "+wHEF.toFixed(precision)+" "+nHEF.toFixed(precision)+"n";
				}
			}
			
			file.save(exData,fileName);
		}
	}
}

导出后处理数据的函数，到处设置的函数。

网格剖分及节点数组定义。

注意边界条件的处理，这个是重点。

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说到这里，就近乎尾声了。