/* nag_pde_parab_1d_euler_exact (d03pxc) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd03.h>
#include <nagx01.h>
#include <math.h>

/* Structure to communicate with user-supplied function arguments */

struct user
{
  double elo, ero, rlo, rro, ulo, uro, gamma;
};

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL bndary(Integer, Integer, double, const double[],
                            const double[], Integer, const double[],
                            const double[], Integer, double[], Integer *,
                            Nag_Comm *);

static void NAG_CALL numflx(Integer, double, double, Integer, const double[],
                            const double[], const double[], double[],
                            Integer *, Nag_Comm *, Nag_D03_Save *);

#ifdef __cplusplus
}
#endif

#define U(I, J)  u[npde*((J) -1)+(I) -1]
#define UE(I, J) ue[npde*((J) -1)+(I) -1]


int main(void)
{
  const Integer npde = 3, npts = 141, ncode = 0, nxi = 0;
  const Integer neqn = npde*npts+ncode, lisave = neqn+24, intpts = 9;
  const Integer nwkres = npde*(2*npts+3*npde+32)+7*npts+4, lenode = 9*neqn+50;
  const Integer mlu = 3*npde-1, lrsave = (3*mlu+1)*neqn+nwkres+lenode;
  double        d, p, tout, ts, v;
  Integer       exit_status = 0, i, ind, itask, itol, itrace, k;
  double        *algopt = 0, *atol = 0, *rtol = 0, *u = 0, *ue = 0, *rsave = 0;
  double        *x = 0, *xi = 0;
  Integer       *isave = 0;
  NagError      fail;
  Nag_Comm      comm;
  Nag_D03_Save  saved;
  struct user   data;

  INIT_FAIL(fail);

  printf(
          "nag_pde_parab_1d_euler_exact (d03pxc) Example Program Results\n");


  /* Allocate memory */

  if (!(algopt = NAG_ALLOC(30, double)) ||
      !(atol = NAG_ALLOC(1, double)) ||
      !(rtol = NAG_ALLOC(1, double)) ||
      !(u = NAG_ALLOC(npde*npts, double)) ||
      !(ue = NAG_ALLOC(npde*intpts, double)) ||
      !(rsave = NAG_ALLOC(lrsave, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(xi = NAG_ALLOC(1, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }

  /* Skip heading in data file */

  scanf("%*[^\n] ");


  /* Problem parameters */

  data.gamma = 1.4;
  data.rlo = 5.99924;
  data.rro = 5.99242;
  data.ulo = 5.99924*19.5975;
  data.uro = -5.99242*6.19633;
  data.elo = 460.894/(data.gamma-1.0) + 0.5*data.rlo*19.5975*19.5975;
  data.ero = 46.095 /(data.gamma-1.0) + 0.5*data.rro*6.19633*6.19633;
  comm.p = (Pointer)&data;

  /* Initialise mesh */

  for (i = 0; i < npts; ++i) x[i] = i/(npts-1.0);

  /* Initial values */

  for (i = 1; i <= npts; ++i)
    {
      if (x[i-1] < 0.5)
        {
          U(1, i) = data.rlo;
          U(2, i) = data.ulo;
          U(3, i) = data.elo;
        }
      else if (x[i-1] == 0.5)
        {
          U(1, i) = 0.5*(data.rlo + data.rro);
          U(2, i) = 0.5*(data.ulo + data.uro);
          U(3, i) = 0.5*(data.elo + data.ero);
        }
      else
        {
          U(1, i) = data.rro;
          U(2, i) = data.uro;
          U(3, i) = data.ero;
        }
    }

  itrace = 0;
  itol = 1;
  atol[0] = 0.005;
  rtol[0] = 5e-4;
  xi[0] = 0.0;
  ind = 0;
  itask = 1;
  for (i = 0; i < 30; ++i) algopt[i] = 0.0;

  /* Theta integration */

  algopt[0] = 2.0;
  algopt[5] = 2.0;
  algopt[6] = 2.0;

  /* Max. time step */

  algopt[12] = 0.005;

  ts = 0.0;
  tout = 0.035;

  /* nag_pde_parab_1d_cd_ode (d03plc).
   * General system of convection-diffusion PDEs with source
   * terms in conservative form, coupled DAEs, method of
   * lines, upwind scheme using numerical flux function based
   * on Riemann solver, one space variable
   */
  nag_pde_parab_1d_cd_ode(npde, &ts, tout, NULLFN, numflx, bndary, u, npts, x,
                          ncode, NULLFN, nxi, xi, neqn, rtol, atol, itol,
                          Nag_TwoNorm, Nag_LinAlgBand, algopt, rsave, lrsave,
                          isave, lisave, itask, itrace, 0, &ind, &comm, &saved,
                          &fail);

  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_pde_parab_1d_cd_ode (d03plc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\n t = %6.3f\n\n", ts);
  printf("%15s%18s%22s\n", "d", "v", "p");
  printf("%3s%10s%9s%9s%9s%11s%11s\n", "x", "Approx", "Exact",
          "Approx", "Exact", "Approx", "Exact");

  /* Read exact data at output points */

  for (i = 1; i <= intpts; ++i)
    {
      scanf("%lf", &UE(1, i));
      scanf("%lf", &UE(2, i));
      scanf("%lf", &UE(3, i));
    }

  /* Calculate density, velocity and pressure */

  k = 0;
  for (i = 15; i <= 127; i += 14)
    {
      ++k;
      d = U(1, i);
      v = U(2, i)/d;
      p = d*(data.gamma-1.0)*(U(3, i)/d - 0.5*v*v);
      printf("%4.1f", x[i-1]);
      printf("%9.4f", d);
      printf("%9.4f", UE(1, k));
      printf("%9.4f", v);
      printf("%9.4f", UE(2, k));
      printf("%13.4e", p);
      printf("%13.4e\n", UE(3, k));
    }

  printf("\n");
  printf(" Number of time steps           = %6ld\n", isave[0]);
  printf(" Number of function evaluations = %6ld\n", isave[1]);
  printf(" Number of Jacobian evaluations = %6ld\n", isave[2]);
  printf(" Number of iterations           = %6ld\n", isave[4]);

 END:

  if (algopt) NAG_FREE(algopt);
  if (atol) NAG_FREE(atol);
  if (rtol) NAG_FREE(rtol);
  if (u) NAG_FREE(u);
  if (ue) NAG_FREE(ue);
  if (rsave) NAG_FREE(rsave);
  if (x) NAG_FREE(x);
  if (xi) NAG_FREE(xi);
  if (isave) NAG_FREE(isave);

  return exit_status;
}


static void NAG_CALL bndary(Integer npde, Integer npts, double t,
                            const double x[], const double u[], Integer ncode,
                            const double v[], const double vdot[],
                            Integer ibnd, double g[], Integer *ires,
                            Nag_Comm *comm)
{
  struct user *data = (struct user *) comm->p;

  if (ibnd == 0)
    {
      g[0] = U(1, 1) - data->rlo;
      g[1] = U(2, 1) - data->ulo;
      g[2] = U(3, 1) - data->elo;
    }
  else
    {
      g[0] = U(1, npts) - data->rro;
      g[1] = U(2, npts) - data->uro;
      g[2] = U(3,
               npts) - data->ero;
    }
  return;
}

static void NAG_CALL numflx(Integer npde, double t, double x, Integer ncode,
                            const double v[], const double uleft[],
                            const double uright[], double flux[],
                            Integer *ires, Nag_Comm *comm, Nag_D03_Save *saved)
{
  struct user *data = (struct user *) comm->p;
  NagError    fail;
  Integer     niter = 0;
  double      tol = 0.0;

  INIT_FAIL(fail);

  /* nag_pde_parab_1d_euler_exact (d03pxc).
   * Exact Riemann Solver for Euler equations in conservative
   * form, for use with nag_pde_parab_1d_cd (d03pfc),
   * nag_pde_parab_1d_cd_ode (d03plc) and
   * nag_pde_parab_1d_cd_ode_remesh (d03psc)
   */
  nag_pde_parab_1d_euler_exact(uleft, uright, data->gamma, tol, niter, flux,
                               saved, &fail);

  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_pde_parab_1d_euler_exact (d03pxc).\n%s\n",
              fail.message);
    }

  return;
}