Description
PDE & Numerical Analysis Seminar
Date and Time: 12th October 2018, at 4PM
Venue: Ramanujan Hall, Mathematics Department.
Speaker: Samala Rathan, VNIT, Nagpur.
Title: "High-resolution shock capturing high-order WENO schemes for hyperbolic conservation laws"
Abstract of the seminar:
"In this talk, we present a class of new higher order WENO spatial approximation
schemes to solve the hyperbolic conservation laws along with the use of total
variation diminishing (TVD)/strong stability preserving Runge-Kutta (SSPRK)
temporial derivative approximation techniques. The objective of these developments
aim for the improvements, in obtaining higher resolution and efficiency of the
solution which retains the desired order of accuracy in smooth regions and in the
presence of critical points. These improvements have been achieved by mainly
focusing on the construction of new smoothness indicators which plays a key role in
the spatial derivative approximation of flux function via the nonlinear weights in WENO
algorithm. With these new measurements, higher-order WENO schemes viz fifth and
seventh-order WENO schemes have been constructed and subsequently imposed a
sufficient condition on the parameters in the weight functions which recovers the
optimal order for smooth regions of solution that includes the critical points.
Numerical results show that these new schemes achieve optimal-order of accuracy.
These schemes also show the advantage of resolving the sharper results for shock
waves, contact discontinuities and the regions that contain high-frequency waves."