The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the interpolation. The original ENO method is constructed based on the polynomial interpolation and the overall rate of convergence provided by the method is uniquely...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...

This paper has analyzed the weights of the 5th order WENO (weighted essentially non-oscillatory) scheme suggested by Jiang and Shu and a modified smoothness estimator is suggested to improve the accuracy. Several numerical tests are presented to demonstrate the accuracy and robustness of the new scheme.

The accurate prediction of blade tip vortices continues to be challenging for the investigation rotor aerodynamics. In current work, vortex system a Caradonna–Tung in hovering state is simulated on account framework high-order WENO scheme and hybrid RANS/LES method progressively. With RANS based fifth-order WENO–Roe scheme, spatial resolution wake age capture accuracy are improved significantly...

In this paper, we propose a well-balanced fifth-order finite difference Hermite WENO (HWENO) scheme for the shallow water equations with non-flat bottom topography in pre-balanced form. For achieving property, adopt similar idea of WENO-XS (Xing and Shu (2005) [30]) to balance flux gradients source terms. The fluxes original are reconstructed by nonlinear HWENO reconstructions while other deriv...

For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusi...

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifthorder WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of t...

A low diffusion E-CUSP (LDE) scheme for preconditioned Navier-Stokes equations is developed. With unfactored implicit Gauss-Seidel relaxation scheme for time integration, the LDE scheme with high-order WENO reconstruction is used to simulate several flows at various speed from low speed natural convection to supersonic flows. Numerical results are presented to show efficiency, accuracy and robu...