From eb43e1a396c2c7c199ee06cac0fa158dc60b7391 Mon Sep 17 00:00:00 2001
From: Matt Strapp <matt@mattstrapp.net>
Date: Wed, 15 Sep 2021 16:34:06 -0500
Subject: Add C file

---
 csci5451/ass1p6.c | 93 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 93 insertions(+)
 create mode 100644 csci5451/ass1p6.c

(limited to 'csci5451/ass1p6.c')

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;
+}
-- 
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