DEVELOPMENT AND TESTING OF THE MODIFIED SIMPSON’S RULE FOR DISCRETE ORDINATES TRANSPORT APPLICATIONS

A new angular quadrature type termed Modified Simpson Trapezoidal (MST) is developed based on the conventional Simpson’s 1/3 rule where pattern over polar levels has a trapezoid shape. An adaptive coefficient correction scheme to enable our integrate flux subintervals separated by interior jump irregularities. two-dimensional test problem employed verify discretization error in uncollided S N scalar computed with sets, as well types. Numerical results show that MST point-wise converges second order against increasing number of discrete angles, while obtained other types slower than first depending regularity exact flux. In reduce points needed, variant quadrature, namely MSTP30, using Quadruple Range [1] fixed 30 angles and applying azimuthal dependence each level. The MSTP30 sets fourth because sufficiently reduced behaves like one-dimensional quadrature. Furthermore, computes integral keep true solution’s irregularity at boundaries, this convergence rate unaffected such inevitable