All-regime Lagrangian-Remap numerical schemes for the gas dynamics equations. Applications to the large friction and low Mach coefficients

In this talk, we propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

Drag & drop

Drag & Drop es una aplicación web diseñada para la creación de problemas a partir de piezas, en la que al profesor se le plantea una nueva posibilidad de evaluar a sus alumnos. La aplicación web servirá como un entorno dedicado a la elaboración de preguntas y respuestas. Para responder a dichas preguntas, se proporcionan unos elementos llamados “piezas” al alumno que se encargará de utilizar para construir su respuesta. A su vez, el profesor al elaborar la pregunta establecerá la solución ideal del problema y el conjunto de “piezas” que los alumnos podrán utilizar para crear las suyas propias. El alumno al terminar la solución de un problema, la enviará al servidor. Este se encargará de evaluarla y comparar la solución del alumno con la solución ideal propuesta por el profesor. Finalmente el profesor será el encargado de examinar el ejercicio y ajustar la calificación, ya sea aceptando la que propone el sistema o indicando una propia.