This work is devoted to the design of boundary controls physical systems that are described by semilinear hyperbolic balance laws. A computational framework presented yields sufficient conditions for a control steer system towards desired state. The approach based on Lyapunov stability analysis and CWENO-type reconstruction.

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

This article aims at developing a high order pressure-based solver for the solution of 3D compressible Navier-Stokes system all Mach numbers. We propose cell-centered discretization governing equations that splits fluxes into fast and slow scale part, are treated implicitly explicitly, respectively. A novel semi-implicit is proposed kinetic energy as well enthalpy in equation, hence avoiding an...

We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000) pp. 241–282]. The method is derived inde...

Some new nonlinear analytical solutions are found for axisymmetric horizontal flows dominated by strong heat sources. These flows are common in multiscale atmospheric and oceanic flows such as hurricane embryos and ocean gyres. The analytical solutions are illustrated with several examples. The proposed exact solutions provide analytical support for previous numerical observations and can be al...

In this work, we present a family of time and space high order finite volume schemes for the solution full Boltzmann equation. The velocity is approximated by using discrete ordinate approach while collisional integral spectral methods. reconstruction implemented integrating distribution function, which describes state system, over arbitrarily shaped closed control volumes Central Weighted ENO ...