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| -rw-r--r-- | csci5451/ass1p6.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/csci5451/ass1p6.c b/csci5451/ass1p6.c new file mode 100644 index 0000000..3b4a1bb --- /dev/null +++ b/csci5451/ass1p6.c @@ -0,0 +1,93 @@ +#include <stdio.h> +#include <stdlib.h> +// HEAT TRANSFER SIMULATION +// +// Simple physical simulation of a rod connected at the left and right +// ends to constant temperature heat/cold sources. All positions on +// the rod are set to an initial temperature. Each time step, that +// temperature is altered by computing the difference between a cells +// temperature and its left and right neighbors. A constant k +// (thermal conductivity) adjusts these differences before altering +// the heat at a cell. Use the following model to compute the heat +// for a position on the rod according to the finite difference +// method. +// +// left_diff = H[t][p] - H[t][p-1]; +// right_diff = H[t][p] - H[t][p+1]; +// delta = -k*( left_diff + right_diff ) +// H[t+1][p] = H[t][p] + delta +// +// Substituting the above, one can get the following +// +// H[t+1][p] = H[t][p] + k*H[t][p-1] - 2*k*H[t][p] + k*H[t][p+1] +// +// The matrix H is computed for all time steps and all positions on +// the rod and displayed after running the simulation. The simulation +// is run for a fixed number of time steps rather than until +// temperatures reach steady state. + +int main(int argc, char **argv) { + int max_time = 50; // Number of time steps to simulate + int width = 20; // Number of cells in the rod + double initial_temp = 50.0; // Initial temp of internal cells + double L_bound_temp = 20.0; // Constant temp at Left end of rod + double R_bound_temp = 80.0; // Constant temp at Right end of rod + double k = 0.5; // thermal conductivity constant + double **H; // 2D array of temps at times/locations + + // Allocate memory + H = malloc(sizeof(double *) * max_time); + int t, p; + for (t = 0; t < max_time; t++) { + H[t] = malloc(sizeof(double *) * width); + } + + // Initialize constant left/right boundary temperatures + for (t = 0; t < max_time; t++) { + H[t][0] = L_bound_temp; + H[t][width - 1] = R_bound_temp; + } + + // Initialize temperatures at time 0 + t = 0; + for (p = 1; p < width - 1; p++) { + H[t][p] = initial_temp; + } + + // Simulate the temperature changes for internal cells + for (t = 0; t < max_time - 1; t++) { + for (p = 1; p < width - 1; p++) { + double left_diff = H[t][p] - H[t][p - 1]; + double right_diff = H[t][p] - H[t][p + 1]; + double delta = -k * (left_diff + right_diff); + H[t + 1][p] = H[t][p] + delta; + } + } + + // Print results + printf("Temperature results for 1D rod\n"); + printf("Time step increases going down rows\n"); + printf("Position on rod changes going accross columns\n"); + + // Column headers + printf("%3s| ", ""); + for (p = 0; p < width; p++) { + printf("%5d ", p); + } + printf("\n"); + printf("%3s+-", "---"); + for (p = 0; p < width; p++) { + printf("------"); + } + printf("\n"); + // Row headers and data + for (t = 0; t < max_time; t++) { + printf("%3d| ", t); + for (p = 0; p < width; p++) { + printf("%5.1f ", H[t][p]); + } + printf("\n"); + } + + return 0; +} |