Second-order central reconstruction in physical space.
Uses a 3-point stencil (half_stencil = 2, stencil_width = 3). For the positive (left-biased) stencil (indices: 1={i-1}, 2={i}, 3={i+1}): F_hat^+ = 0.5 * (F^+i + F^+) = 0.5*(stencil(:,2) + stencil(:,3))
For the reversed negative stencil (indices: 1={i+2}, 2={i+1}, 3={i}): F_hat^- = 0.5 * (F^-_{i+1} + F^-_i) = 0.5*(stencil(:,2) + stencil(:,3)) [identical formula; sum is commutative]
Total numerical flux = F_hat^+ + F_hat^- = 0.5*(F_i + F_{i+1}).
WARNING: Zero numerical dissipation. Stable only for smooth, periodic problems within the CFL stability region. Do not use for discontinuous or non-periodic problems.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in) | :: | f_stencil(:,:) | |||
| real(kind=wp), | intent(out) | :: | f_hat(:) |