An efficient implementation technique of a block matrix implicit operator based on van Leer’s FVS
scheme is proposed for the LU-SGS method on unstructured meshes. The off-diagonal terms of
the linear system of equations were approximated by the increment of the numerical flux using the
point-by-point splitting feature of FVS schemes. The present improved LU-SGS method provides
better performance in terms of CPU time and requires substantially less storage than the corresponding
baseline method. The convergence rate of the present improved method is faster than
the improved method based on the Jameson and Turkel implicit operator.