Numerical analysis of FDV method for one-dimensional Euler equations - Bin Zulkafli, Mohd Fadhli; Omar, Ashraf Ali E.; Asrar, Waqar (2012)
Finite volume form of Flowfield Dependent Variation (FDV) method was implemented into upwind scheme in order to solve one-dimensional Euler equations. The implementation of FDV method was motivated by its ability in solving the transition and interaction between different flow regimes based on the so-called FDV parameters which are dependent to the physical properties of the flow. Finite volume form was chosen to add capabilities of handling complex geometries with the advantages of relatively low computational memories requirement. In the present work, conservative variables were approximated using high resolution MUSCL scheme and minmod limiter. Stability condition of the method was analyzed using Von Neumann analysis and has found to be conditionally stable. The accuracy of the method was tested by solving shock tube problem and the results matched with analytical solution.