English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A new gridding technique for the solution of partial differential equationsin cubical geometry is presented. The method is based on volume penalization,allowing for the imposition of a cubical geometry inside of its circumscribingsphere. By choosing to embed the cube inside of the sphere, one obtains adiscretization that is free of any sharp edges or corners. Taking fulladvantage of the simple geometry of the sphere, spectral bases based onspin-weighted spherical harmonics and Jacobi polynomials, which properlycapture the regularity of scalar, vector and tensor components in sphericalcoordinates, can be applied to obtain moderately efficient and accuratenumerical solutions of partial differential equations in the cube. Thistechnique demonstrates the advantages of these bases over other methods forsolving PDEs in spherical coordinates. We present results for a test case ofincompressible hydrodynamics in cubical geometry: Rayleigh-B\'enard convectionwith fully Dirichlet boundary conditions. Analysis of the simulations provideswhat is, to our knowledge, the first result on the scaling of the heat fluxwith the thermal forcing for this type of convection in a cube in a sphere.

The "Sphered Cube": A New Method for the Solution of Partial Differential Equations in Cubical Geometry