Diffusion/diffusion_v0.c

// 包括库	--- Include libraries
#include <stdio.h>
#include <math.h>

// 定义		--- Definitions
#define N 256 		// 空间网格数	--- Number of spatial grid points
#define T 255		// 时间步数   	--- Time steps to be simulated (integrated)
#define dt 1 		// 时间步长	--- Temporal length scale (dt)
#define dx 1 		// 空间步长	--- Spatial length scale （dx
#define alpha 0.5 	// 扩散系数	--- Diffusion coefficient


// 全球结构	--- Global structures
struct simulation_data{
	double u[N];	// u： 为当前时刻的浓度分
			//      --- To store the concentration distribution at the current moment
	int generation;	// generation: 模拟迭代	--- simulation iteration 
	} state;


// 打印功能	--- Print function (truncated)
void printGrid(double grid[N], int time) {
	// 代	--- generations
	printf("[dt x  %d]\t", time);
	// 最左边3个格点的状态	--- state of the 3 left-most lattice sites
	for (int i = 0; i < 3;i++){
		 printf("%.2f ", grid[i]);
                 printf("\t");
		}
	printf("...\t");
	// 三个中心格点的状态	--- state of the 3 center lattice sites
        for (int i = floor(N/2)-1 ; i < floor(N/2)+2;i++){
                 printf("%.2f ", grid[i]);
                 printf("\t");
                }
	printf("...\t");
	// 3个最右边格点的状态	--- state of the 3 right-most lattice sites
	for (int i = N-3; i < N;i++){
                 printf("%.2f ", grid[i]);
                 printf("\t");
		}
	printf("\n");
	}


// 初始化功能	--- Initialization function
void init_lattice(void){
	// 初始化浓度分布	--- Initialize concentration distribution
	for (int i = 0; i < N; i++) {
        	if (i >= 45*N/100 && i <= 55*N/100) {
            	state.u[i] = 100.0;
        	} else {
            	state.u[i] = 0.0;
        	}
    	}
	// 初始化时间		--- Initialize time
    	state.generation = 0;
	}


// 更新功能	--- Update function (to increment one iteration/generation)
void update_lattice(void){
	// u_new： 为下一个时刻的浓度分布
	double u_new[N];//      --- To store the concentration distribution at the next moment
	// 强制边界条件		--- Enforce boundary condition
	u_new[0] = state.u[0];
        u_new[N] = state.u[N];
	// 内部节点计算         --- Internal node calculation
        for (int i = 1; i < N; i++) {
            	u_new[i] = state.u[i] + alpha * dt / (dx*dx) * (state.u[i+1] - 2*state.u[i] + state.u[i-1]);
        	}
	// 更新浓度分布         --- Update concentration distribution
        for (int i = 0; i < N; i++) {
		state.u[i] = u_new[i];
        	}
        //printGrid(state.u,state.generation);
        state.generation ++;
	}

// 模拟	--- simulation
void integrate_simulation(void){
	// 初始化模拟           --- Initialize simulation
        init_lattice();
	printGrid(state.u, state.generation);
	// 迭代计算		--- Iterative calculation
        for (int t = 1; t <= T; t++) {
        	update_lattice();
        	printGrid(state.u, state.generation);
        	}
	}


// 主要功能	--- Main function
int main(int    argc, char **argv) {
	integrate_simulation();
    	return 0;
	}