scholarly journals The global classical solution to compressible Euler system with velocity alignment

2020 ◽  
Vol 5 (6) ◽  
pp. 6673-6692
Author(s):  
Lining Tong ◽  
◽  
Li Chen ◽  
Simone Göttlich ◽  
Shu Wang ◽  
...  
Keyword(s):  
Classical Solution ◽  
Euler System ◽  
Global Classical Solution ◽  
Compressible Euler

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals Blowup of Solutions to the Compressible Euler-Poisson and Ideal MHD Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wenming Hu
Keyword(s):  
Finite Time ◽  
Euler System ◽  
Time Dependent ◽  
Poisson System ◽  
Blowup Of Solutions ◽  
Finite Time Blowup ◽  
Ideal Mhd ◽  
Compressible Euler ◽  
Time Blowup

In the present paper, we study the blowup of the solutions to the full compressible Euler system and pressureless Euler-Poisson system with time-dependent damping. By some delicate analysis, some Riccati-type equations are achieved, and then, the finite time blowup results can be derived.

scholarly journals Linear Stability Analysis of Runge–Kutta-Based Partial Time-Splitting Schemes for the Euler Equations

2010 ◽  
Vol 138 (12) ◽  
pp. 4475-4496 ◽  
Author(s):  
Michael Baldauf
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Simulation Models ◽  
Euler System ◽  
Splitting Schemes ◽  
Stability Properties ◽  
Compressible Euler ◽  
Numerical Stability Analysis ◽  
Time Splitting ◽  
Runge Kutta

Abstract For atmospheric simulation models with resolutions from about 10 km to the subkilometer cloud-resolving scale, the complete nonhydrostatic compressible Euler equations are often used. An important integration technique for them is the time-splitting (or split explicit) method. This article presents a comprehensive numerical stability analysis of Runge–Kutta (RK)-based partial time-splitting schemes. To this purpose a linearized two-dimensional (2D) compressible Euler system containing advection (as the slow process), sound, and gravity wave terms (as fast processes) is considered. These processes are the most important ones in limiting stability. First, the detailed stability properties are discussed with regard to several off-centering weights for each fast process described by horizontally explicit, vertically implicit schemes. Then the stability properties of the temporally and spatially discretized three-stage RK scheme for the complete 2D Euler equations and their stabilization (e.g., by divergence damping) are discussed. The main goal is to find optimal values for all of the occurring numerical parameters to guarantee stability in operational model applications. Furthermore, formal orders of temporal truncation errors for the time-splitting schemes are calculated. With the same methodology, two alternatives to the three-stage RK method, a so-called RK3-TVD method, and a new four-stage, second-order RK method are inspected.

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