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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE)finite volume scheme on unstructured triangular meshes that is high orderaccurate in space and time and that also allows for time-accurate local timestepping (LTS). The new scheme uses the following basic ingredients: a highorder WENO reconstruction in space on unstructured meshes, an element-localhigh-order accurate space-time Galerkin predictor that performs the timeevolution of the reconstructed polynomials within each element, the computationof numerical ALE fluxes at the moving element interfaces through approximateRiemann solvers, and a one-step finite volume scheme for the time update whichis directly based on the integral form of the conservation equations inspace-time. The inclusion of the LTS algorithm requires a number of crucialextensions, such as a proper scheduling criterion for the time update of eachelement and for each node; a virtual projection of the elements contained inthe reconstruction stencils of the element that has to perform the WENOreconstruction; and the proper computation of the fluxes through the space-timeboundary surfaces that will inevitably contain hanging nodes in time due to theLTS algorithm. We have validated our new unstructured Lagrangian LTS approachover a wide sample of test cases solving the Euler equations of compressiblegasdynamics in two space dimensions, including shock tube problems, cylindricalexplosion problems, as well as specific tests typically adopted in Lagrangiancalculations, such as the Kidder and the Saltzman problem. When compared to thetraditional global time stepping (GTS) method, the newly proposed LTS algorithmallows to reduce the number of element updates in a given simulation by afactor that may depend on the complexity of the dynamics, but which can be aslarge as 4.7.

High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes