In this paper an analysis of the global AAM conservation properties of NCAR’s Community Atmosphere Model Spectral Element (CAM-SE) dynamical core under HeldSuarez forcing is presented. It is shown that the spurious sources/sinks of AAM in CAMSE are three orders of magnitude smaller than the parameterized (physical) sources/sinks. The effect on AAM conservation by changing various numerical aspe...

A definition of even and odd matrices is given, and some of their elementary properties stated. The basic result is that if λ is an eigenvalue of an odd matrix, then so is −λ. Starting from this, there is a consideration of some ways of using odd matrices to test the order of accuracy of eigenvalue routines. 1. Definitions and some elementary properties Let us call a matrix W even if its elemen...

The minimized dispersion and controllable dissipation (MDCD) reconstruction technique optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation. A low dispersion finite volume scheme based on MDCD reconstruction is proposed which is capable of handling flow discontinuities and resolving a broad range of length scales. Although the proposed...

—For a randomized stochastic optimization algorithm, consistency conditions of estimates are slackened and the order of accuracy for a finite number of observations is studied. A new method of realization of this algorithm on quantum computers is developed.

A fast and accurate algorithm for the reinitialization of the signed distance function in two and three spatial dimensions is presented. The algorithm has computational complexity O(N logN) for the reinitialization of N grid points. The order of accuracy of the reinitialization is demonstrated to depend primarily on the interpolation algorithm used. Bicubic interpolation is demonstrated to resu...

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immers...

In this paper we carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order of accuracy and non-oscillatory properties of the new schemes. Compared to the state-of-art finite...

We extend the technique of optimal time step (OTS) selection for finite difference (FD) schemes of time dependent PDEs to PDEs where the leading-order spatial derivative term has a spatially varying coefficient. The basic approach involves identifying a transformation of the domain that eliminates the spatial dependence of the coefficient for the leading-order term. This change of variables is ...

The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error. In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investi...

Spectral deferred corrections (SDC) is an iterative approach for constructing higherorder accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equati...