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The stability analysis for a model problem is discussed.

In Section 2, the bilinear state space model problem is stated along with underlying assumptions.

A model problem is considered and a finite difference discretization for that model is described.

The model problem is considered for a subsonic flow in a moving fluid.

A 2D model problem is used to illustrate the difficulties encountered.

The crucial item of the DG formulation of the model problem is the treatment of the convection part.

Numerical results for a model problem are reported to demonstrate the efficiency of the sparse solver.

The stability and convergence properties predicted by the model problem are then compared to those obtained in the CHT computation.

A model problem was set up for complicated physical phenomena, such as multi-phase flow, multiple gas species, flow in a porous medium, and conjugate heat transfer.

Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.

The transport equations for the model problem are simplified using lubrication theory, and a convergent finite-difference method is formulated to obtain solutions to the simplified equation set.