In this work a new class of numerical methods for the BGK model of kinetic equations is presented. In principle, schemes of any order of accuracy in both space and time can be constructed with this technique. The methods proposed are based on an explicit-implicit time discretization. In particular the convective terms are treated explicitly, while the source terms are implicit. In this fashion ...

In combination with simultaneous approximation terms, summation-by-parts (SBP) operators provide a flexible and efficient methodology that leads to consistent, conservative, and provably stable high-order discretizations. Traditional diagonal-norm SBP operators with a repeating interior point operator lead to solutions that have a global order of accuracy lower than the order of the interior po...

Gasdynamic features of slowly rotating gas axisymmetric accretion onto a gravitating center are investigated. The process of flow restructuring is studied as the angular velocity of accreting matter approaches the Keplerian angular velocity. For spherically-symmetric accretion, the conditions are found of the existence of a steady-state supersonic solution for various external boundary conditio...

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...

Abstract: The use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed. Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. When a fracti...

Knowledge of a truncated Fourier series expansion for a 2nperiodic function of finite regularity, which is assumed to be piecewise smooth in each period, is used to accurately reconstruct the corresponding function. An algebraic equation of degree M is constructed for the M singularity locations in each period for the function in question. The M coefficients in this algebraic equation are obtai...

In this paper, we propose a functional fitting s-stage Runge-Kutta method which is based on the exact integration of the set of the linearly independent functions u i (t), (i = 1,. .. , s). The method is exact when the solution of the ODE can be expressed as the linear combination of u i (t), although the method has an error for general ODE. In this work we investigate the order of accuracy of ...

Weighted essentially non-oscillatory (WENO) methods can simultaneously provide the high order of accuracy, high bandwidth-resolving efficiency, and shock-capturing capability required for the detailed simulation of compressible turbulence. However, rigorous analysis of the actual versus theoretical error properties of these non-linear numerical methods is difficult. We use a bandwidth-optimized...

We derive a bound on the order of accuracy for interpolation schemes used in energy stable summation-by-parts discretizations on non-conforming multiblock grids. This result explains the suboptimal accuracy of such schemes reported in previous works. Numerical simulations confirm a corresponding reduced convergence rate in both maximum and L2 norms.

First order errors downstream of shocks have been detected in computations with higher order shock capturing schemes in one and two dimensions. Based on a matched asymptotic expansion analysis we show how to modify the artificial viscosity and raise the order of accuracy.