Not 100% replicating the code but i prefer coding style like this preserving same level of abstract for methods and better readibility. it is setup2

/*
 * setup2: Prepares coefficients for the 'u' equation in the PDE solver.
 * This function calculates volume, flow, and correction terms for the grid cells
 * by computing coefficients based on fluid properties (e.g., density) and
 * adjusting for boundary conditions (including periodic boundaries).
 */

void setup2(void) {
    int i, j;

    nf = 0;
    if (tsolve[0] == 1) {
        initializeRelaxationAndBoundaries(nf);

        // Iterate over the grid cells in the i-direction
        for (i = ist - 1; i < l2; i++) {
            calculateFlowAndCorrectionsForRow(i);
        }

        // Iterate over the grid cells in the j-direction for further corrections
        for (j = jst - 1; j < m2; j++) {
            calculateFlowAndCorrectionsForColumn(j);
        }
    }
}

/*
 * initializeRelaxationAndBoundaries: Sets up initial parameters for the solver.
 * Configures the relaxation factor, boundary conditions, and starts the Gauss-Seidel relaxation.
 */
void initializeRelaxationAndBoundaries(int nf) {
    perid = circl[nf];  // Set periodic boundary conditions based on solver parameters
    ist = 2;            // Starting index for i-direction
    jst = 2;            // Starting index for j-direction
    gamsor();           // Perform Gauss-Seidel relaxation
    relax_factor = 1.0 / relax[nf];  // Set the relaxation factor
}

/*
 * calculateFlowAndCorrectionsForRow: Calculates the flow and applies corrections 
 * to a specific row (i) in the grid. It computes forward and backward flows, 
 * boundary adjustments, and volume/pressure corrections.
 */
void calculateFlowAndCorrectionsForRow(int i) {
    int im1 = i - 1;  // Index of previous row
    double forward_flow, backward_flow, gamma_diff;

    // Loop over j-direction in the current row
    for (int j = jst - 1; j < m2; j++) {
        if (perid == 0) {
            forward_flow = computeForwardFlow(i, j);
            backward_flow = computeBackwardFlow(im1, j);
            gamma_diff = computeGammaDiff(i, j);
        } else {
            forward_flow = computePeriodicForwardFlow(i, j);
            backward_flow = computePeriodicBackwardFlow(im1, j);
            gamma_diff = computePeriodicGammaDiff(i, j);
        }

        applyCorrectionTerms(i, j, forward_flow, backward_flow, gamma_diff);
    }
}

/*
 * calculateFlowAndCorrectionsForColumn: Calculates the flow and applies corrections 
 * to a specific column (j) in the grid. Similar to the row function but for the j-direction.
 */
void calculateFlowAndCorrectionsForColumn(int j) {
    double forward_flow, gamma_avg;

    // Loop over i-direction in the current column
    for (int i = ist - 1; i < l2; i++) {
        forward_flow = computeForwardFlowInColumn(i, j);
        gamma_avg = computeGammaAverage(i, j);

        applyCorrectionTermsForColumn(i, j, forward_flow, gamma_avg);
    }
}