/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                              
*/
//  Shock.java: Formation of Shockwave from Burger's eqnt

import java.io.*;

public class shock  {
  
  public static void main(String[] argv)
                         throws IOException, FileNotFoundException {
													 
    PrintWriter w = new PrintWriter         //  Output into Shock.dat
                           (new FileOutputStream("Shock.dat"), true);
    PrintWriter q =                     // initial conditions in file
          new PrintWriter(new FileOutputStream("initial.dat"), true);
					
    int m = 100; // number of grid points
    double u[] = new double[m+1];                   // Final solution
    double u0[] = new double[m+1];                    // Initial data
    double epsilon = 1.0;                               // Wave speed
    double beta = 0.1;                                  // CFL number
    double x, dx, dt, T_final;
    int i, j, n;
		
    dx = 2.0/m;                                         // Space step
    dt = beta*dx/epsilon;                                // Time step
    T_final = 0.15;
    n=(int)(T_final/dt);System.out.println(""+n+"");
		                                              // Initial solution
    for ( i=0; i < m-1; i++ )  {                           
       x = i*dx;
       u0[i] = 3.0*Math.sin(3.2*x);
       q.println(""+0.01*i+" "+u0[i]+" ");  
    }
		                                           // Lax-Wendroff scheme
    for ( j=1;j < n;j++)  {                       
      for ( i=0;i < m-1;i++ )  {
        u[i+1] = u0[i+1]-(u0[i+2]*u0[i+2] - u0[i]*u0[i])*(0.25*beta)+
         +(((u0[i+2]+u0[i+1])/2.0)*(u0[i+2]*u0[i+2]-u0[i+1]*u0[i+1])-
                 ((u0[i+1]+u0[i])/2.0)*(u0[i+1]*u0[i+1]-u0[i]*u0[i]))
                                                     *0.25*beta*beta;
        u[0]=0.0; u[m-1]=0.0;
        if ( j%5==0 && i%4==0 )  w.println(" "+u[i]);
				                                          // Shift new to old
        u0[i] = u[i];                                 
      }
      if ( j%5 == 0) w.println("");
    }
    System.out.println("Numerical solution data saved in Shock.dat");
  }                                                           // Main
}                                                            // Class