// Use.
void table_center (const GeometryRect& geo,
const std::vector<double>& Density, Treelog& msg)
{
// Print it.
const size_t column_size = geo.cell_columns ();
const size_t row_size = geo.cell_rows ();
std::ostringstream tmp;
// Top line
tmp << "z\\x";
for (size_t col = 0; col < column_size; col++)
{
daisy_assert (row_size > 0);
tmp << "\t" << geo.cell_x (geo.cell_index (0, col));
}
// Rows.
for (size_t row = 0; row < row_size; row++)
{
daisy_assert (column_size > 0);
tmp << "\n" << geo.cell_z (geo.cell_index (row, 0));
for (size_t col = 0; col < column_size; col++)
{
const size_t cell = geo.cell_index (row, col);
daisy_assert (cell < Density.size ());
tmp << "\t" << Density[cell];
}
}
Treelog::Open nest (msg, "Root density table [(cm, cm) -> cm/cm^3]");
msg.message (tmp.str ());
}
void
UZRectMollerup::drain (const GeometryRect& geo,
const std::vector<size_t>& drain_cell,
const double drain_water_level,
const ublas::vector<double>& h,
const ublas::vector<double>& Theta_previous,
const ublas::vector<double>& Theta,
const ublas::vector<double>& S_vol,
#ifdef TEST_OM_DEN_ER_BRUGT
const ublas::vector<double>& S_macro,
#endif
const ublas::vector<double>& dq,
const double& ddt,
std::vector<bool>& drain_cell_on,
Solver::Matrix& A,
ublas::vector<double>& b,
const int debug, Treelog& msg)
{
const size_t drain_size = drain_cell.size (); // // number of drains
std::ostringstream tmp;
for (size_t d = 0; d < drain_size; d++)
{
const size_t cell = drain_cell[d];
// Pressure in drain cell [cm].
const double drain_h = drain_water_level - geo.cell_z (cell);
if (drain_cell_on[d]) //drain on
{
//Calculate fluxes to drain from last timestep
double drain_sink = Theta_previous (cell);
drain_sink -= Theta (cell);
drain_sink -= ddt * (S_vol (cell)
#ifdef TEST_OM_DEN_ER_BRUGT
+ S_macro (cell)
#endif
)/
geo.cell_volume (cell);
const std::vector<size_t>& edges = geo.cell_edges (cell);
const size_t edge_size = edges.size ();
for (size_t i = 0; i < edge_size; i++)
{
const size_t edge = edges[i];
const double flux = dq (edge) * geo.edge_area (edge) * ddt;
const int from = geo.edge_from (edge);
const int to = geo.edge_to (edge);
if (cell == from)
drain_sink -= flux / geo.cell_volume (cell);
else if (cell == to)
drain_sink += flux / geo.cell_volume (cell);
}
if (drain_sink <= 0.0)
drain_cell_on[d] = false;
}
else // drain off
if (h (cell) > 0.0)
drain_cell_on[d] = true;
if (drain_h > 0.0 || drain_cell_on[d] == true)
{
const std::vector<size_t>& edges = geo.cell_edges (cell);
const size_t edge_size = edges.size ();
// Force pressure to be zero.
for (size_t i = 0; i < edge_size; i++)
{
const size_t edge = edges[i];
if (!geo.edge_is_internal (edge))
continue;
const size_t other = geo.edge_other (edge, cell);
A (cell, other) = 0.0;
}
A (cell, cell) = 1.0;
b (cell) = std::max (drain_h, 0.0);
}
}
}
void
UZRectMollerup::upperboundary (const GeometryRect& geo,
const Soil& soil,
const ublas::vector<double>& T,
const Surface& surface,
std::vector<top_state>& state,
const ublas::vector<double>& remaining_water,
const ublas::vector<double>& h,
const ublas::vector<double>& Kedge,
ublas::vector<double>& dq,
ublas::banded_matrix<double>& Dm_mat,
ublas::vector<double>& Dm_vec,
ublas::vector<double>& Gm,
ublas::vector<double>& B,
const double ddt,
const int debug,
Treelog& msg, const double BIG_DT)
{
const std::vector<size_t>& edge_above = geo.cell_edges (Geometry::cell_above);
const size_t edge_above_size = edge_above.size ();
for (size_t i = 0; i < edge_above_size; i++)
{
const size_t edge = edge_above[i];
const int cell = geo.edge_other (edge, Geometry::cell_above);
daisy_assert (geo.cell_is_internal (cell));
const double in_sign
= geo.cell_is_internal (geo.edge_to (edge)) ? 1.0 : -1.0;
daisy_assert (in_sign < 0);
const double area = geo.edge_area (edge);
const double sin_angle = geo.edge_sin_angle (edge);
switch (surface.top_type (geo, edge))
{
case Surface::forced_flux:
{
const double flux = -surface.q_top (geo, edge, BIG_DT);
Neumann (edge, cell, area, in_sign, flux, dq, B);
}
break;
case Surface::forced_pressure:
{
const double value = -Kedge (edge) * geo.edge_area_per_length (edge);
const double pressure = surface.h_top (geo, edge);
Dirichlet (edge, cell, area, in_sign, sin_angle,
Kedge (edge),
h (cell), value, pressure, dq, Dm_mat, Dm_vec, Gm);
}
break;
case Surface::limited_water:
{
const double h_top = remaining_water (i);
// We pretend that the surface is particlaly saturated.
const double K_sat = soil.K (cell, 0.0, 0.0, T (cell));
const double K_cell = Kedge (edge);
const double K_edge = 0.5 * (K_cell + K_sat);
const double dz = geo.edge_length (edge);
daisy_assert (approximate (dz, -geo.cell_z (cell)));
double q_in_avail = h_top / ddt;
const double q_in_pot = K_edge * (h_top - h (cell) + dz) / dz;
// Decide type.
bool is_flux = h_top <= 0.0 || q_in_pot > q_in_avail;
if (is_flux)
{
state[i] = top_flux;
Neumann (edge, cell, area, in_sign, q_in_avail, dq, B);
}
else // Pressure
{
state[i] = top_pressure;
if (debug > 0 && q_in_pot < 0.0)
{
std::ostringstream tmp;
tmp << "q_in_pot = " << q_in_pot << ", q_avail = "
<< q_in_avail << ", h_top = " << h_top
<< ", h (cell) = " << h (cell)
<< " K (edge) = " << Kedge (edge)
<< ", K_sat = " << K_sat << ", K_edge = "
<< K_edge <<", dz = " << dz << ", ddt = " << ddt
<< ", is_flux = " << is_flux << "\n";
msg.message (tmp.str ());
}
const double value = -K_edge * geo.edge_area_per_length (edge);
const double pressure = h_top;
Dirichlet (edge, cell, area, in_sign, sin_angle,
K_edge, h (cell),
value, pressure, dq, Dm_mat, Dm_vec, Gm);
}
if (debug == 3)
{
std::ostringstream tmp;
tmp << "edge = " << edge << ", K_edge = " << K_edge
<< ", h_top = "
<< h_top << ", dz = " << dz << ", q_avail = " << q_in_avail
<< ", q_pot = " << q_in_pot << ", is_flux = " << is_flux;
msg.message (tmp.str ());
}
}
break;
case Surface::soil:
throw "Don't know how to handle this surface type";
default:
daisy_panic ("Unknown surface type");
}
}
}
void
UZRectMollerup::tick (const GeometryRect& geo,
const std::vector<size_t>& drain_cell,
const double drain_water_level,
const Soil& soil,
SoilWater& soil_water, const SoilHeat& soil_heat,
const Surface& surface, const Groundwater& groundwater,
const double dt, Treelog& msg)
{
daisy_assert (K_average.get ());
const size_t edge_size = geo.edge_size (); // number of edges
const size_t cell_size = geo.cell_size (); // number of cells
// Insert magic here.
ublas::vector<double> Theta (cell_size); // water content
ublas::vector<double> Theta_previous (cell_size); // at start of small t-step
ublas::vector<double> h (cell_size); // matrix pressure
ublas::vector<double> h_previous (cell_size); // at start of small timestep
ublas::vector<double> h_ice (cell_size); //
ublas::vector<double> S (cell_size); // sink term
ublas::vector<double> S_vol (cell_size); // sink term
#ifdef TEST_OM_DEN_ER_BRUGT
ublas::vector<double> S_macro (cell_size); // sink term
std::vector<double> S_drain (cell_size, 0.0); // matrix-> macro -> drain flow
std::vector<double> S_drain_sum (cell_size, 0.0); // For large timestep
const std::vector<double> S_matrix (cell_size, 0.0); // matrix -> macro
std::vector<double> S_matrix_sum (cell_size, 0.0); // for large timestep
#endif
ublas::vector<double> T (cell_size); // temperature
ublas::vector<double> Kold (edge_size); // old hydraulic conductivity
ublas::vector<double> Ksum (edge_size); // Hansen hydraulic conductivity
ublas::vector<double> Kcell (cell_size); // hydraulic conductivity
ublas::vector<double> Kold_cell (cell_size); // old hydraulic conductivity
ublas::vector<double> Ksum_cell (cell_size); // Hansen hydraulic conductivity
ublas::vector<double> h_lysimeter (cell_size);
std::vector<bool> active_lysimeter (cell_size);
const std::vector<size_t>& edge_above = geo.cell_edges (Geometry::cell_above);
const size_t edge_above_size = edge_above.size ();
ublas::vector<double> remaining_water (edge_above_size);
std::vector<bool> drain_cell_on (drain_cell.size (),false);
for (size_t i = 0; i < edge_above_size; i++)
{
const size_t edge = edge_above[i];
remaining_water (i) = surface.h_top (geo, edge);
}
ublas::vector<double> q; // Accumulated flux
q = ublas::zero_vector<double> (edge_size);
ublas::vector<double> dq (edge_size); // Flux in small timestep.
dq = ublas::zero_vector<double> (edge_size);
//Make Qmat area diagonal matrix
//Note: This only needs to be calculated once...
ublas::banded_matrix<double> Qmat (cell_size, cell_size, 0, 0);
for (int c = 0; c < cell_size; c++)
Qmat (c, c) = geo.cell_volume (c);
// make vectors
for (size_t cell = 0; cell != cell_size ; ++cell)
{
Theta (cell) = soil_water.Theta (cell);
h (cell) = soil_water.h (cell);
h_ice (cell) = soil_water.h_ice (cell);
S (cell) = soil_water.S_sum (cell);
S_vol (cell) = S (cell) * geo.cell_volume (cell);
if (use_forced_T)
T (cell) = forced_T;
else
T (cell) = soil_heat.T (cell);
h_lysimeter (cell) = geo.zplus (cell) - geo.cell_z (cell);
}
// Remember old value.
Theta_error = Theta;
// Start time loop
double time_left = dt; // How much of the large time step left.
double ddt = dt; // We start with small == large time step.
int number_of_time_step_reductions = 0;
int iterations_with_this_time_step = 0;
int n_small_time_steps = 0;
while (time_left > 0.0)
{
if (ddt > time_left)
ddt = time_left;
std::ostringstream tmp_ddt;
tmp_ddt << "Time t = " << (dt - time_left)
<< "; ddt = " << ddt
<< "; steps " << n_small_time_steps
<< "; time left = " << time_left;
Treelog::Open nest (msg, tmp_ddt.str ());
if (n_small_time_steps > 0
&& (n_small_time_steps%msg_number_of_small_time_steps) == 0)
{
msg.touch ();
msg.flush ();
}
n_small_time_steps++;
if (n_small_time_steps > max_number_of_small_time_steps)
{
msg.debug ("Too many small timesteps");
throw "Too many small timesteps";
}
// Initialization for each small time step.
if (debug > 0)
{
std::ostringstream tmp;
tmp << "h = " << h << "\n";
tmp << "Theta = " << Theta;
msg.message (tmp.str ());
}
int iterations_used = 0;
h_previous = h;
Theta_previous = Theta;
if (debug == 5)
{
std::ostringstream tmp;
tmp << "Remaining water at start: " << remaining_water;
msg.message (tmp.str ());
}
ublas::vector<double> h_conv;
for (size_t cell = 0; cell != cell_size ; ++cell)
active_lysimeter[cell] = h (cell) > h_lysimeter (cell);
for (size_t edge = 0; edge != edge_size ; ++edge)
{
Kold[edge] = find_K_edge (soil, geo, edge, h, h_ice, h_previous, T);
Ksum [edge] = 0.0;
}
std::vector<top_state> state (edge_above.size (), top_undecided);
// We try harder with smaller timesteps.
const int max_loop_iter
= max_iterations * (number_of_time_step_reductions
* max_iterations_timestep_reduction_factor + 1);
do // Start iteration loop
{
h_conv = h;
iterations_used++;
std::ostringstream tmp_conv;
tmp_conv << "Convergence " << iterations_used;
Treelog::Open nest (msg, tmp_conv.str ());
if (debug == 7)
msg.touch ();
// Calculate conductivity - The Hansen method
for (size_t e = 0; e < edge_size; e++)
{
Ksum[e] += find_K_edge (soil, geo, e, h, h_ice, h_previous, T);
Kedge[e] = (Ksum[e] / (iterations_used + 0.0)+ Kold[e]) / 2.0;
}
//Initialize diffusive matrix
Solver::Matrix diff (cell_size);
// diff = ublas::zero_matrix<double> (cell_size, cell_size);
diffusion (geo, Kedge, diff);
//Initialize gravitational matrix
ublas::vector<double> grav (cell_size); //ublass compatibility
grav = ublas::zero_vector<double> (cell_size);
gravitation (geo, Kedge, grav);
// Boundary matrices and vectors
ublas::banded_matrix<double> Dm_mat (cell_size, cell_size,
0, 0); // Dir bc
Dm_mat = ublas::zero_matrix<double> (cell_size, cell_size);
ublas::vector<double> Dm_vec (cell_size); // Dir bc
Dm_vec = ublas::zero_vector<double> (cell_size);
ublas::vector<double> Gm (cell_size); // Dir bc
Gm = ublas::zero_vector<double> (cell_size);
ublas::vector<double> B (cell_size); // Neu bc
B = ublas::zero_vector<double> (cell_size);
lowerboundary (geo, groundwater, active_lysimeter, h,
Kedge,
dq, Dm_mat, Dm_vec, Gm, B, msg);
upperboundary (geo, soil, T, surface, state, remaining_water, h,
Kedge,
dq, Dm_mat, Dm_vec, Gm, B, ddt, debug, msg, dt);
Darcy (geo, Kedge, h, dq); //for calculating drain fluxes
//Initialize water capacity matrix
ublas::banded_matrix<double> Cw (cell_size, cell_size, 0, 0);
for (size_t c = 0; c < cell_size; c++)
Cw (c, c) = soil.Cw2 (c, h[c]);
std::vector<double> h_std (cell_size);
//ublas vector -> std vector
std::copy(h.begin (), h.end (), h_std.begin ());
#ifdef TEST_OM_DEN_ER_BRUGT
for (size_t cell = 0; cell != cell_size ; ++cell)
{
S_macro (cell) = (S_matrix[cell] + S_drain[cell])
* geo.cell_volume (cell);
}
#endif
//Initialize sum matrix
Solver::Matrix summat (cell_size);
noalias (summat) = diff + Dm_mat;
//Initialize sum vector
ublas::vector<double> sumvec (cell_size);
sumvec = grav + B + Gm + Dm_vec - S_vol
#ifdef TEST_OM_DEN_ER_BRUGT
- S_macro
#endif
;
// QCw is shorthand for Qmatrix * Cw
Solver::Matrix Q_Cw (cell_size);
noalias (Q_Cw) = prod (Qmat, Cw);
//Initialize A-matrix
Solver::Matrix A (cell_size);
noalias (A) = (1.0 / ddt) * Q_Cw - summat;
// Q_Cw_h is shorthand for Qmatrix * Cw * h
const ublas::vector<double> Q_Cw_h = prod (Q_Cw, h);
//Initialize b-vector
ublas::vector<double> b (cell_size);
//b = sumvec + (1.0 / ddt) * (Qmatrix * Cw * h + Qmatrix *(Wxx-Wyy));
b = sumvec + (1.0 / ddt) * (Q_Cw_h
+ prod (Qmat, Theta_previous-Theta));
// Force active drains to zero h.
drain (geo, drain_cell, drain_water_level,
h, Theta_previous, Theta, S_vol,
#ifdef TEST_OM_DEN_ER_BRUGT
S_macro,
#endif
dq, ddt, drain_cell_on, A, b, debug, msg);
try {
solver->solve (A, b, h); // Solve Ah=b with regard to h.
} catch (const char *const error) {
std::ostringstream tmp;
tmp << "Could not solve equation system: " << error;
msg.warning (tmp.str ());
// Try smaller timestep.
iterations_used = max_loop_iter + 100;
break;
}
for (int c=0; c < cell_size; c++) // update Theta
Theta (c) = soil.Theta (c, h (c), h_ice (c));
if (debug > 1)
{
std::ostringstream tmp;
tmp << "Time left = " << time_left << ", ddt = " << ddt
<< ", iteration = " << iterations_used << "\n";
tmp << "B = " << B << "\n";
tmp << "h = " << h << "\n";
tmp << "Theta = " << Theta;
msg.message (tmp.str ());
}
for (int c=0; c < cell_size; c++)
{
if (h (c) < min_pressure_potential || h (c) > max_pressure_potential)
{
std::ostringstream tmp;
tmp << "Pressure potential out of realistic range, h["
<< c << "] = " << h (c);
msg.debug (tmp.str ());
iterations_used = max_loop_iter + 100;
break;
}
}
}
while (!converges (h_conv, h) && iterations_used <= max_loop_iter);
if (iterations_used > max_loop_iter)
{
number_of_time_step_reductions++;
if (number_of_time_step_reductions > max_time_step_reductions)
{
msg.debug ("Could not find solution");
throw "Could not find solution";
}
iterations_with_this_time_step = 0;
ddt /= time_step_reduction;
h = h_previous;
Theta = Theta_previous;
}
else
{
// Update dq for new h.
ublas::banded_matrix<double> Dm_mat (cell_size, cell_size,
0, 0); // Dir bc
Dm_mat = ublas::zero_matrix<double> (cell_size, cell_size);
ublas::vector<double> Dm_vec (cell_size); // Dir bc
Dm_vec = ublas::zero_vector<double> (cell_size);
ublas::vector<double> Gm (cell_size); // Dir bc
Gm = ublas::zero_vector<double> (cell_size);
ublas::vector<double> B (cell_size); // Neu bc
B = ublas::zero_vector<double> (cell_size);
lowerboundary (geo, groundwater, active_lysimeter, h,
Kedge,
dq, Dm_mat, Dm_vec, Gm, B, msg);
upperboundary (geo, soil, T, surface, state, remaining_water, h,
Kedge,
dq, Dm_mat, Dm_vec, Gm, B, ddt, debug, msg, dt);
Darcy (geo, Kedge, h, dq);
#ifdef TEST_OM_DEN_ER_BRUGT
// update macropore flow components
for (int c = 0; c < cell_size; c++)
{
S_drain_sum[c] += S_drain[c] * ddt/dt;
S_matrix_sum[c] += S_matrix[c] * ddt/dt;
}
#endif
std::vector<double> h_std_new (cell_size);
std::copy(h.begin (), h.end (), h_std_new.begin ());
// Update remaining_water.
for (size_t i = 0; i < edge_above.size (); i++)
{
const int edge = edge_above[i];
const int cell = geo.edge_other (edge, Geometry::cell_above);
const double out_sign = (cell == geo.edge_from (edge))
? 1.0 : -1.0;
remaining_water[i] += out_sign * dq (edge) * ddt;
daisy_assert (std::isfinite (dq (edge)));
}
if (debug == 5)
{
std::ostringstream tmp;
tmp << "Remaining water at end: " << remaining_water;
msg.message (tmp.str ());
}
// Contribution to large time step.
daisy_assert (std::isnormal (dt));
daisy_assert (std::isnormal (ddt));
q += dq * ddt / dt;
for (size_t e = 0; e < edge_size; e++)
{
daisy_assert (std::isfinite (dq (e)));
daisy_assert (std::isfinite (q (e)));
}
for (size_t e = 0; e < edge_size; e++)
{
daisy_assert (std::isfinite (dq (e)));
daisy_assert (std::isfinite (q (e)));
}
time_left -= ddt;
iterations_with_this_time_step++;
if (iterations_with_this_time_step > time_step_reduction)
{
number_of_time_step_reductions--;
iterations_with_this_time_step = 0;
ddt *= time_step_reduction;
}
}
// End of small time step.
}
// Mass balance.
// New = Old - S * dt + q_in * dt - q_out * dt + Error =>
// 0 = Old - New - S * dt + q_in * dt - q_out * dt + Error
Theta_error -= Theta; // Old - New
Theta_error -= S * dt;
#ifdef TEST_OM_DEN_ER_BRUGT
for (size_t c = 0; c < cell_size; c++)
Theta_error (c) -= (S_matrix_sum[c] + S_drain_sum[c]) * dt;
#endif
for (size_t edge = 0; edge != edge_size; ++edge)
{
const int from = geo.edge_from (edge);
const int to = geo.edge_to (edge);
const double flux = q (edge) * geo.edge_area (edge) * dt;
if (geo.cell_is_internal (from))
Theta_error (from) -= flux / geo.cell_volume (from);
if (geo.cell_is_internal (to))
Theta_error (to) += flux / geo.cell_volume (to);
}
// Find drain sink from mass balance.
#ifdef TEST_OM_DEN_ER_BRUGT
std::fill(S_drain.begin (), S_drain.end (), 0.0);
#else
std::vector<double> S_drain (cell_size);
#endif
for (size_t i = 0; i < drain_cell.size (); i++)
{
const size_t cell = drain_cell[i];
S_drain[cell] = Theta_error (cell) / dt;
Theta_error (cell) -= S_drain[cell] * dt;
}
if (debug == 2)
{
double total_error = 0.0;
double total_abs_error = 0.0;
double max_error = 0.0;
int max_cell = -1;
for (size_t cell = 0; cell != cell_size; ++cell)
{
const double volume = geo.cell_volume (cell);
const double error = Theta_error (cell);
total_error += volume * error;
total_abs_error += std::fabs (volume * error);
if (std::fabs (error) > std::fabs (max_error))
{
max_error = error;
max_cell = cell;
}
}
std::ostringstream tmp;
tmp << "Total error = " << total_error << " [cm^3], abs = "
<< total_abs_error << " [cm^3], max = " << max_error << " [] in cell "
<< max_cell;
msg.message (tmp.str ());
}
// Make it official.
for (size_t cell = 0; cell != cell_size; ++cell)
soil_water.set_content (cell, h (cell), Theta (cell));
#ifdef TEST_OM_DEN_ER_BRUGT
soil_water.add_tertiary_sink (S_matrix_sum);
soil_water.drain (S_drain_sum, msg);
#endif
for (size_t edge = 0; edge != edge_size; ++edge)
{
daisy_assert (std::isfinite (q[edge]));
soil_water.set_flux (edge, q[edge]);
}
soil_water.drain (S_drain, msg);
// End of large time step.
}