  In this article, the construction and implementation of a seventh order
weighted essentially non-oscillatory scheme is reported for hyperbolic
conservation laws. Local smoothness indicators are constructed based on
$L_{1}$-norm, where a higher order interpolation polynomial is used with each
derivative being approximated to the fourth order of accuracy with respect to
the evaluation point. The global smoothness indicator so constructed ensures
the scheme achieves the desired order of accuracy. The scheme is reviewed in
the presence of critical points and verified the numerical accuracy,
convergence with the help of linear scalar test cases. Further, the scheme is
implemented to non-linear scalar and system of equations in one and two
dimensions. As the formulation is based on method of lines, to move forward in
time linear strong-stability-preserving Runge-Kutta scheme (lSSPRK) for the
linear problems and the fourth order nonlinear version of five stage strong
stability preserving Runge-Kutta scheme (SSPRK(5,4)) for nonlinear problems is
used.
