Abstract
We propose a bi-dimensional finite volume extension of a continuous ALE method on unstructured cells whose edges are parameterized by rational quadratic Bezier curves. For each edge, the control point possess a weight that permits to represent any conic (see for example [LIGACH]) and thanks to [WAGUSEDE,WAGU], we are able to compute the exact area of our cells. We then give an extension of scheme for remapping step based on volume fluxing [MARSHA] and self-intersection flux [ALE2DHAL]. For the rezoning phase, we propose a three step process based on moving nodes, followed by control point and weight re-adjustment. Finally, for the hydrodynamic step, we present the GLACE scheme [GLACE] extension (at first-order) on conic cell using the same formalism. We only propose some preliminary first-order simulations for each steps: Remap, Pure Lagrangian and finally ALE (rezoning and remapping).
Highlights
The prototype system of interest is the Euler system written in ux forms
The third section is the rezoning step of ALE on conic cells for which we propose to move the control points after moving the nodes with standard algorithm
We construct the rst-order GLACE hydrodynamic scheme, and show some numerical examples for pure Lagrangian and ALE tests in the last section
Summary
The prototype system of interest is the Euler system written in ux forms. Written over a frame moving. Such systems are discretized on polygonal type cells. We recall the exact ux formula in [WAGUSEDE, WAGU] used to compute the area of a cell with an arbitrary number of conic edges, we reinterpret the area in terms of nodal/control point contributions like in GLACE formalism [GLACE] giving a rst step toward the design of hydrodynamic conic GLACE scheme. The third section is the rezoning step of ALE on conic cells for which we propose to move the control points after moving the nodes with standard (polygonal) algorithm. We construct the rst-order GLACE hydrodynamic scheme, and show some numerical examples for pure Lagrangian and ALE tests in the last section
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
