As atmospheric models are pushed towards non-hydrostatic resolutions, there is a growing need for new numerical discretizations that are accurate, robust and effective at these scales. In this paper we describe a new arbitrary-order staggered nodal finite-element method (SNFEM) vertical discretization motivated by flux reconstruction methods. The SNFEM formulation generalizes traditional second...

Two new formulations of a symmetric WENO method for the direct numerical simulation of compressible turbulence are presented. The schemes are designed to maximize order of accuracy and bandwidth, while minimizing dissipation. The formulations and the corresponding coefficients are introduced. Numerical solutions to canonical flow problems are used to determine the dissipation and bandwidth prop...

the arthroscopic study of knee joint is of outstanding interest in assessment of knee complaints. the present article describes the results of arthroscopic examination of 100 patients (mean age 29.4 years 82% male) evaluated from 1996 to 1997 in imam khomeini hospital of tehran. sport injury was the most prevalent cause of referral (40%). the 2 most frequent complaints were knee pain (94%) and ...

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.

Combined with simultaneous approximation terms, summation-by-parts (SBP) operators o↵er a versatile and e cient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed su↵er from a loss of accuracy. While on the interior, these operators are of degree 2p...

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.

One of the visualization problems implies finding boundaries and insides of flat sections of 3D objects specified analytically. This problem is to be solved to analyze the results and to control the geometry specification. On the one hand, the analytic definition of profiles for “not simple” 3D-objects in general case is actually unsolvable problem; on the other hand, it is necessary to apply v...

We derive a bound on the order of accuracy of interpolation operators for energy stable summation-by-parts discretizations on non-conforming multiblock meshes. The new theoretical result, which corroborate with experience from previous work, implies a local reduction in the formal accuracy of summation-by-parts discretizations based on diagonal norms. Numerical results confirm a corresponding r...

This work concentrates upon the Mimetic discretization of elliptic partial differential equations (PDE). Numerical solutions are obtained and discussed for one-dimensional ODE on uniform and irregular grids and two-dimensional PDE on uniform grids. The focal point is to develop a scheme that incorporates the full tensor case on uniform grids in 2-D. The numerical results are then compared to pr...