A high order particle-source-in-cell (PSIC) algorithm is presented for the computation of the interaction between shocks, small scale structures, and liquid and/or solid particles in high-speed engineering applications. The improved high order finite difference weighted essentially non-oscillatory (WENO-Z) method for solution of the hyperbolic conservation laws that govern the shocked carrier g...

We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus this work is nonlinear stabilization continuous Galerkin (CG) approximations. proposed methodology also provides an interesting alternative to WENO-based limiters discontinuous (DG) methods. Unlike Runge–Kutta DG sche...

High Mach number astrophysical jets are simulated using a positive scheme, and are compared with WENO-LF simulations. A version of the positive scheme has allowed us to simulate astrophysical jets with radiative cooling up to Mach number 270 with respect to the heavy jet gas, a factor of two times higher than the maximum Mach number attained with the WENO schemes and ten times higher than with ...

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes. We use the Lax-Friedrichs monotone flux as building blocks, third order reconstructions made from combinations of linear polynomials which are constructed on div...

In order to simulate accurately the interaction of shock wave/complex flows, hybrid schemes combining the compact scheme and weighted essentially non-oscillatory(WENO) scheme are beneficial, especially the high order low diffusion schemes used in smooth regions. There are two key issues, one is how to detect the discontinuity, the other is how to choose the high order low diffusion scheme to en...

The two-phase drift flux model is extensively used in multiphase flow applications. In this study, we focus on possible numerical schemes for solving the model. Due to complexity of primitive equations and empirical parameters, it challenging achieve stability scheme high resolution second order central scheme, central-upwind third fifth weighted essentially non-oscillatory (WENO) were successf...

A fifth order weighted essentially non-oscillatory (WENO) fast sweeping method is designed in this paper, extending the result of the third order WENO fast sweeping method in J. Sci. Comput. 29, 25–56 (2006) and utilizing the two approaches of accurate inflow boundary condition treatment in J. Comput. Math. 26, 1–11 (2008), which allows the usage of Cartesian meshes regardless of the domain bou...

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [14] to convection diffusion equations, we propose a non-conventional high order finite volume weighted essentially non-oscillatory (WENO) scheme which can be proven maximum-principle-satisfying. Two-dimensional extensions are straightforward. We also show that the same idea can be used to construct hi...

Computational fluid dynamics simulations using the WENO method and level set method are applied to high Mach number nonrelativistic astrophysical jets, including the effects of radiative cooling. WENO methods introduced in Liu et al. (J. Comput. Phys., 115:200–212, 1994) have allowed us to simulate HH 1-2 astrophysical jets at Mach number much higher than Mach 80 (Ha et al. in J. Sci. Comput. 2...