Evaluation Of Spatial Derivatives Research Articles

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.

An adaptive finite volume solver for ice sheets and glaciers

We have developed a new adaptive finite volume scheme for numerical simulations of ice sheets and glaciers. The mathematical basis of the adaptive solver is represented by the finite volume method and irregular Voronoi cell grids. Evaluation of spatial derivatives are obtained at cell edges from approximating the ice surface elevation locally by second‐order polynomials following a least squares approach. The proposed scheme includes a simple and accurate method for handling discontinuities in ice thickness gradients along ice margins. The flexibility of the Voronoi cell structure allows for local mesh refinement in selected areas. We show how increased mesh density along a steep ice margin may considerably increase overall numerical accuracy of an ice sheet simulation. Although the numerical scheme is not restricted to ice sheet representations using the shallow ice approximation (SIA), we here use analytical SIA solutions to test the accuracy of the method.

Neural network tool for rapid recovery of plasma topology

A general method for the rapid recovery of plasma topology based on a neural network fit of the normalized magnetic flux is presented. We propose a general method for coordinate inversions that is based on a neural network fit of the normalized magnetic flux. The neural network provides a flexible and compact base for representing the plasma topology and allows the evaluation of spatial derivatives by analytic methods (as opposed to finite-difference methods), making it faster than other techniques. We present examples of this technique for both two-dimensional plasmas (tokamak D shaped, X point) and stellarators.

Optimized compact finite difference schemes with maximum resolution

Direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high-resolution characteristics in the evaluation of spatial derivatives. Compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders. An analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes, based on the idea of the minimization of dispersive (phase) errors in the wave number domain, and these are applied to the analytic optimization of multidiagonal compact schemes. Actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections, and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases, respectively. From these comparisons, the usefulness of an optimized high-order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed. For the optimized high-order spatial schemes, the feasibility of using classical high-order Runge-Kutta time advancing methods is investigated.