The weighted essentially non-oscillatory schemes are higher-order accurate spatial reconstruction techniques which are commonly used to simulate compressible flows due to their capability to capture small structures with a high resolution and resolving shocks in a non-oscillatory manner. The WENO scheme was proposed by Liu et al. in finite volume framework, and later it was extended in the finite-difference framework by Jiang and Shu. During the last two decades, the WENO schemes have witnessed tremendous development in terms of improvements and extensions to many complex model problems. A wide spectrum of WENO schemes is now available in the literature. Recently we have developed a new fifth and seventh-order WENO scheme of adaptive order for 2D problems. Here, we would like to develop a new efficient version of the WENO scheme of adaptive order for the following model problem in 3D.

Publication:

• Asha K. Dond, Rakesh Kumar “Finite difference modified WENO schemes for hyperbolic conservation laws with non-convex flux”. International Journal For Numerical Methods In Fluids, 2021

• Ameya D. Jagtap, Rakesh Kumar, “Kinetic theory based improved multi-level adaptive finite difference WENO schemes for compressible Euler equations”. Wave Motion, 98, 2020

• Asha Kumari Meena, Rakesh Kumar, Praveen Chandrashekar, “Positivity- preserving finite difference WENO scheme for Ten-Moment equations with source term”, Journal of Scientific Computing, 82, 2020.

• Rakesh Kumar, Praveen Chandrashekar, “Efficient seventh order WENO schemes of adaptive order for hyperbolic conservation laws.”, Computers & Fluids, 190, 49-76, 2019.

• Rakesh Kumar, Praveen Chandrashekar, “Simple smoothness indicator and multi-level adaptive order WENO scheme for hyperbolic conservation laws”, Journal of Computational Physics, 375, 1059-1090, 2018.