Record number :
1560427
Title of article :
On a regularization of the compressible Euler equations for an isothermal gas
Author/Authors :
Bhat، نويسنده , , H.S. and Fetecau، نويسنده , , R.C.، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2009
Pages :
14
From page :
168
To page :
181
Abstract :
We consider a Leray-type regularization of the compressible Euler equations for an isothermal gas. The regularized system depends on a small parameter α > 0 . Using Riemann invariants, we prove the existence of smooth solutions for the regularized system for every α > 0 . The regularization mechanism is a non-linear bending of characteristics that prevents their finite-time crossing. We prove that, in the α → 0 limit, the regularized solutions converge strongly. However, based on our analysis and numerical simulations, the limit is not the unique entropy solution of the Euler equations. The numerical method used to support this claim is derived from the Riemann invariants for the regularized system. This method is guaranteed to preserve the monotonicity of characteristics.
Keywords :
compressible Euler equations , Leray regularization , Riemann invariants , Isothermal gas
Journal title :
Journal of Mathematical Analysis and Applications
Serial Year :
2009
Link To Document :
بازگشت