A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods

We introduce a polynomial spectral calculus that follows from the summation by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus to simplify the analysis of two multidimensional discontinuous Galerkin spectral element approximations

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented

Spectral collocation methods

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2

Psuedospectral calculation of shock turbulence interactions

A Chebyshev-Fourier discretization with shock fitting is used to solve the unsteady Euler equations. The method is applied to shock interactions with plane waves and with a simple model of homogeneous isotropic turbulence. The plane wave solutions are compared to linear theory

Pseudospectral solution of two-dimensional gas-dynamic problems

Chebyshev pseudospectral methods are used to compute two dimensional smooth compressible flows. Grid refinement tests show that spectral accuracy can be obtained. Filtering is not needed if resolution is sufficiently high and if boundary conditions are carefully prescribed

Spectral methods for the Euler equations: Chebyshev methods and shock-fitting

The Chebyshev spectral collocation method for the Euler gas-dynamic equations is described. It is used with shock fitting to compute several two-dimensional, gas-dynamic flows. Examples include a shock-acoustic wave interaction, a shock/vortex interaction, and the classical blunt body problem. With shock fitting, the spectral method has a clear advantage over second order finite differences in that equivalent accuracy can be obtained with far fewer grid points

The <i>Arabidopsis</i> SGN3/GSO1 receptor kinase integrates soil nitrogen status into shoot development

The Casparian strip is a barrier in the endodermal cell walls of plants that allows the selective uptake of nutrients and water. In the model plant Arabidopsis thaliana, its development and establishment are under the control of a receptor-ligand mechanism termed the Schengen pathway. This pathway facilitates barrier formation and activates downstream compensatory responses in case of dysfunction. However, due to a very tight functional association with the Casparian strip, other potential signaling functions of the Schengen pathway remain obscure. In this work, we created a MYB36-dependent synthetic positive feedback loop that drives Casparian strip formation independently of Schengen-induced signaling. We evaluated this by subjecting plants in which the Schengen pathway has been uncoupled from barrier formation, as well as a number of established barrier-mutant plants, to agar-based and soil conditions that mimic agricultural settings. Under the latter conditions, the Schengen pathway is necessary for the establishment of nitrogen-deficiency responses in shoots. These data highlight Schengen signaling as an essential hub for the adaptive integration of signaling from the rhizosphere to aboveground tissues

The origin of secondary heavy rare earth element enrichment in carbonatites: Constraints from the evolution of the Huanglongpu district, China

publisher: Elsevier articletitle: The origin of secondary heavy rare earth element enrichment in carbonatites: Constraints from the evolution of the Huanglongpu district, China journaltitle: Lithos articlelink: http://dx.doi.org/10.1016/j.lithos.2018.02.027 content_type: article copyright: © 2018 The Authors. Published by Elsevier B.V.Copyright: © 2018 Published by Elsevier B.V. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The file attached is the Published/publisher’s pdf version of the articl

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte