A high order multi-resolution WENO numerical scheme for solving viscous quantum hydrodynamic model for semiconductor devices

Abstract

In this article, fifth order finite volume multi-resolution weighted essentially non-oscillatory (MR-WENO) scheme is developed for solving one-dimensional non linear viscous quantum hydrodynamical model for semiconductor devices with constant temperature. This non linear model consists of three equations, two equations for the current density and electron density, and third equation is the Poisson equation. The first two equations include the viscous and quantum correction terms. Further, numerical technique is used to obtain the solution due to high non linearity of considered model. The multi-resolution technique is used to reduce the computational cost of high resolution numerical scheme. In the procedure of derivation of the MR-WENO scheme unequal central spatial stencils are used and linear weights can be chosen any positive numbers with only restriction that their total sum is one. Various numerical test problems are considered to check the validity and accuracy of the derived numerical scheme. Further, the results obtained from considered numerical scheme are compared with those of kinetic flux vector splitting numerical scheme.

Keywords

• Viscous quantum hydrodynamic
• Semiconductor devices
• Current density
• Multi-resolution
• WENO scheme