Conservative, Shock-capturing Transport Methods with Nonconservative Velocity Approximations

Simulations of transport in one dimension

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Simpli ed Discretization of Systems of Hyperbolic Conservation Laws Containing Advection Equations

The high speed ow of complex materials can often be modeled by the compressible Euler Equations coupled to (possibly many) additional advection equations. Traditionally, good computational results have been obtained by writing these systems in fully conservative form and applying the general methodology of shock-capturing schemes for systems of hyperbolic conservation laws. In this paper, we sh...

Structure-preserving shock-capturing methods: late-time asymptotics, curved geometry, small-scale dissipation, and nonconservative products

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...