/******************************************************************************
* @brief Iterate to find actual shear stress during saltation.
*****************************************************************************/
void
shear_stress(double U10,
double ZO,
double *ushear,
double *Zo_salt,
double utshear)
{
double umin, umax, xacc;
double fl, fh, df;
/* Find min & max shear stress to bracket value. */
umin = utshear;
umax = CONST_KARMAN * U10;
xacc = 0.10 * umin;
/* Check to see if value is bracketed. */
get_shear(umin, &fl, &df, U10, 10.);
get_shear(umax, &fh, &df, U10, 10.);
if (fl < 0.0 && fh < 0.0) {
log_err("Solution surpasses upper boundary."
"fl(%f)=%f, fh(%f)=%f", umin, fl, umax, fh);
}
if (fl > 0.0 && fh > 0.0) {
*Zo_salt = ZO;
*ushear = CONST_KARMAN * U10 / log(10. / ZO);
}
else {
/* Iterate to find actual shear stress. */
*ushear = rtnewt(umin, umax, xacc, U10, 10.);
*Zo_salt = 0.12 * (*ushear) * (*ushear) / (2. * CONST_G);
}
}
void shear_stress(double U10, double ZO,double *ushear, double *Zo_salt, double utshear)
{
double umin, umax, xacc;
double fl, fh, df;
/* Find min & max shear stress to bracket value. */
umin = utshear;
umax = von_K*U10;
xacc = 0.10*umin;
/* Check to see if value is bracketed. */
get_shear(umin,&fl,&df, U10, 10.);
get_shear(umax,&fh,&df, U10, 10.);
if(fl < 0.0 && fh < 0.0) {
fprintf(stderr, "Solution in rtnewt surpasses upper boundary.\n");
fprintf(stderr, "fl(%f)=%f, fh(%f)=%f\n",umin, fl, umax, fh);
exit(0);
}
if(fl > 0.0 && fh > 0.0) {
// fprintf(stderr, "No solution possible that exceeds utshear.\n");
// fprintf(stderr, "utshear=%f, u10=%f\n",utshear, U10);
*Zo_salt = ZO;
*ushear = von_K * U10 / log(10./ZO);
}
else {
/* Iterate to find actual shear stress. */
*ushear = rtnewt (umin, umax, xacc, U10, 10.);
*Zo_salt = 0.12 *(*ushear) * (*ushear) / (2.* G_STD);
}
}
double rtnewt(double x1, double x2, double acc, double Ur, double Zr)
{
int j;
double df, dx, dxold, f, fh, fl;
double temp, xh, xl, rts;
get_shear(x1,&fl,&df, Ur, Zr);
get_shear(x2,&fh,&df, Ur, Zr);
if ((fl > 0.0 && fh > 0.0) || (fl < 0.0 && fh < 0.0)) {
fprintf(stderr, "Root must be bracketed in rtnewt.\n");
exit(0);
}
if (fl == 0.0) return x1;
if (fh == 0.0) return x2;
if (fl < 0.0) {
xl=x1;
xh=x2; }
else {
xh=x1;
xl=x2;
}
rts=0.5*(x1+x2);
dxold=fabs(x2-x1);
dx=dxold;
get_shear(rts,&f,&df, Ur, Zr);
for(j=1; j<=MAX_ITER; j++) {
if((((rts-xh)*df-f)*((rts-x1)*df-f) > 0.0)
|| (fabs(2.0*f) > fabs(dxold*df))) {
dxold=dx;
dx=0.5*(xh-xl);
rts=xl+dx;
if (xl == rts) return rts; }
else {
dxold=dx;
dx=f/df;
temp=rts;
rts -= dx;
if (temp == rts) return rts;
}
if(fabs(dx) < acc) return rts;
// if(rts < .025) rts=.025;
get_shear(rts,&f,&df, Ur, Zr);
if(f<0.0)
xl=rts;
else
xh = rts;
}
fprintf(stderr, "Maximum number of iterations exceeded in rtnewt.\n");
return 0.0;
}
/******************************************************************************
* @brief Newton-Raphson method.
*****************************************************************************/
double
rtnewt(double x1,
double x2,
double acc,
double Ur,
double Zr)
{
extern parameters_struct param;
int j;
double df, dx, dxold, f, fh, fl;
double temp, xh, xl, rts;
get_shear(x1, &fl, &df, Ur, Zr);
get_shear(x2, &fh, &df, Ur, Zr);
if ((fl > 0.0 && fh > 0.0) || (fl < 0.0 && fh < 0.0)) {
log_err("Root must be bracketed");
}
if (fl == 0.0) {
return x1;
}
if (fh == 0.0) {
return x2;
}
if (fl < 0.0) {
xl = x1;
xh = x2;
}
else {
xh = x1;
xl = x2;
}
rts = 0.5 * (x1 + x2);
dxold = fabs(x2 - x1);
dx = dxold;
get_shear(rts, &f, &df, Ur, Zr);
for (j = 1; j <= param.BLOWING_MAX_ITER; j++) {
if ((((rts - xh) * df - f) * ((rts - x1) * df - f) > 0.0) ||
(fabs(2.0 * f) > fabs(dxold * df))) {
dxold = dx;
dx = 0.5 * (xh - xl);
rts = xl + dx;
if (xl == rts) {
return rts;
}
}
else {
dxold = dx;
dx = f / df;
temp = rts;
rts -= dx;
if (temp == rts) {
return rts;
}
}
if (fabs(dx) < acc) {
return rts;
}
// if(rts < .025) rts=.025;
get_shear(rts, &f, &df, Ur, Zr);
if (f < 0.0) {
xl = rts;
}
else {
xh = rts;
}
}
log_err("Maximum number of iterations exceeded");
}