I am trying to re write my code implementing on a C compilator in MATLAB. The aim is to solve using finite volume method the equation below :
With :
I am applying the method such that :
## Code
mandatory declarations: */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/** definition of the field h, the flux Q, time step */
double*x=NULL,*h=NULL,*Q=NULL;
double dt,L0,Delta;
double t;
int i,N;
/** Main with definition of parameters */
int main() {
L0 = 5.;
N = 128;
t=0;
Delta = L0/N;
dt =.0025;
/** dynamic allocation */
x= (double*)calloc(N+1,sizeof(double));
h= (double*)calloc(N+1,sizeof(double));
Q= (double*)calloc(N+1,sizeof(double));
/**
first cell between ‘0-Delta/2‘ and ‘0+Delta/2‘, centred in
ith cell beween ‘(i-1/2) Delta‘ (left) and ‘(i +1/2) Delta‘(right) centered in ‘(i)
*/
for(i=0;i<=N;i++)
{ x[i]=0+(i)*Delta;
h[i] = (1)*(x[i]<1);}
/** begin the time loop */
while(t<=100){
t = t + dt;
/** flux */
for(i=1;i<=N;i++)
Q[i] = - 1./3*pow(((h[i]+h[i-1])/2),3)*(h[i]-h[i-1])/Delta;
/** explicit step update and BC$$h_i^{n+1}=h_i^{n} -{\Delta t} \dfrac{F(Q_{i+1})-
for(i=1;i<N-1;i++)
h[i] += - dt* ( Q[i+1] - Q[i] )/Delta;
h[0]=h[1];
h[N]=h[N-1];
}
/** clean */
free(h);
free(Q);
free(x);
} /**
I am just wondering how to write the Q[I] line in MATLAB because h[I] depends on Q[I].
Thank you in advance,
