[Abstract] In this paper, we introduce a new type of high order shock capturing schemes – uniform weighted compact and non-compact scheme (UWCNC) or simply XJL scheme developed by Xie, Jiang and Liu. This new scheme is based on the feature of discrete data sets instead of the physics. The fundamental task of CFD is to provide an accurate approximation of derivatives for a given discrete data se...

A generalization of the optimization framework typically used in moving least squares is presented that provides high-order approximation while maintaining compact stencils and a consistent treatment of boundaries. The approach, which we refer to as compact moving least squares, resembles the capabilities of compact finite differences but requires no structure in the underlying set of nodes. An...

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by us...

In this paper, we give sixth order compact finite difference formula for second order integro-differential equations (IDE) with different boundary conditions, and both of error estimates and numerical experiments confirm our compact finite difference method can get fifth order of accuracy. We also adjust compact finite difference method for first order IDE and a system of IDE and give numerical...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

a compact and sharp-rejection ultra-wideband (uwb) microstrip bandpass filter (bpf) is presented. the proposed filter is constructed with multiple-mode resonator (mmr) and split ring resonator (srr). moreover, proposed structure consists of two doublets parallel coupling gaps at each side of a microstrip ring. in comparison with some other filters, this structure shows a significantly wider pas...