Chapter 1 Shock capturing methods

Developing a Shock-Capturing Formulation with Higher Performance to Capture Normal Standing Shock in All-Speed Regime

The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we def...

Developing a Shock-Capturing Formulation with Higher Performance to Capture Normal Standing Shock in All-Speed Regime

The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we def...

Shock Capturing and Related Numerical Methods in Computational Fluid Dynamics

Some developments and efforts in designing and analyzing shock capturing algorithms and related numerical methods in computational fluid dynamics are reviewed. The importance of numerical viscosity in shock capturing algorithms is analyzed; the convergence and stability of some shock capturing algorithms are presented; the role of shock capturing algorithms in a mathematical existence theory is...

High-Order Shock-Fitting and front-tracking Methods for Numerical Simulation of Shock-Disturbance Interactions

High-order methods that can resolve interactions of flow-disturbances with shock waves are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. Most of the popular shock-capturing methods are inherently dissipative and may incur numerical oscillations near the shock. Present...

Conservative, Shock-capturing Transport Methods with Nonconservative Velocity Approximations