|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4967058||1449361||2018||18 صفحه PDF||سفارش دهید||دانلود کنید|
Many interesting astrophysical and atmospheric problems involve flows near the hydrostatic equilibrium state where the pressure gradient is balanced by the gravitational force. In this paper, we design high order well-balanced discontinuous Galerkin methods for the Euler equations with gravitation, which can preserve the discrete polytropic and isothermal hydrostatic balance states exactly. To achieve the well-balancedness, we propose to combine the numerical fluxes based on a generalized hydrostatic reconstruction, with an equilibrium state recovery technique and a novel source term approximation. Extensive one- and two-dimensional numerical examples are shown to demonstrate the performance of our well-balanced methods, and comparison with non-well-balanced results is included to illustrate the importance of maintaining the balance between pressure gradient and gravitational force numerically.
Journal: Journal of Computational Physics - Volume 352, 1 January 2018, Pages 445-462