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Energy Estimates for Nonlinear Conservation Laws with Applications to Solutions of the Burgers Equation and One-Dimensional Viscous Flow in a Shock Tube by Central Difference Schemes
Energy Estimates Nonlinear Conservation Laws Applications Solutions Burgers Equation One-Dimensional Viscous Flow
2015/7/2
A prime focus in the development of computational fluid dynamics (CFD) for aeronautics has been the simulation of transonic and supersonic flows which generally contain shock waves, contac...
Energy Estimates for Nonlinear Conservation Laws with Applications to Solutions of the Burgers Equation and One-Dimensional Viscous Flow in a Shock Tube by Central Difference Schemes
Energy Estimates Central Diff erence Schemes
2015/6/18
The use of energy estimates to establish the stability of dis
crete approximations
to initial value problems has a long history. The energy meth
od is discussed in
the classical book by Morton and...
A Space-time Smooth Artificial Viscosity Method For Nonlinear Conservation Laws
Space-time Smooth Artificial Viscosity Method Nonlinear Conservation Laws Computational Physics
2012/4/19
We introduce the $C$-method, a simple scheme for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and cont...
$L^\infty(L^\infty)$-boundedness of DG($p$)-solutions for nonlinear conservation laws with boundary conditions
nonlinear conservation laws boundary conditions
2010/11/18
We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estim...