Title: An improved alternative weighted essentially non-oscillatory scheme for conservation laws

Authors: Uttam Singh Rajput; Krishna Mohan Singh

Addresses: Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India ' Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India

Abstract: In the present study, a fifth-order improved alternative weighted essentially non-oscillatory scheme has been developed for nonlinear hyperbolic conservation laws. We have proposed an improved fifth-order smoothness indicator to design the present scheme. Further, the numerical flux evaluation is based on the reconstruction of primitive variables rather than conservative variables. The third-order TVD Runge-Kutta method has been used for the time advancement of the solution. The computations have been performed for various one, two, and three-dimensional test cases. Numerical results are compared with the exact solution and results with other high-resolution schemes. The proposed scheme resolves the fine-scale structure with a higher resolution. Further, it is computationally efficient, produces less spurious oscillations, and shows better conservation of kinetic energy for 3D Taylor-Green vortex case.

Keywords: alternative WENO scheme; hyperbolic equations; unsteady; numerical fluxes; high-resolution scheme; compressible flow.

DOI: 10.1504/PCFD.2023.134205

Progress in Computational Fluid Dynamics, An International Journal, 2023 Vol.23 No.5, pp.261 - 277

Received: 20 Jul 2021
Received in revised form: 14 Jul 2022
Accepted: 14 Jul 2022
Published online: 13 Oct 2023 *

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