Abstract
The correct modeling for processes involving convection, without introducing excessive artificial damping while retaining high accuracy, stability, boundedness and simplicity of implementation continues being nowadays a challenging task for CFD practitioners. The objective of this study is to present and evaluate the performance of two new upwinding schemes, namely SDPUS-C1 and EPUS, for nonlinear convection term discretization. Both SDPUS-C1 and EPUS schemes satisfy the TVD principle of Harten and are based on the NVD formulation of Leonard. Firstly, a description of the schemes is presented and then the numerical results are provided for one- and two-dimensional hyperbolic conservation laws. Finally, as an application, the SDPUS-C1 and EPUS schemes are employed for the simulation of two-dimensional incompressible fluid flows involving moving free surfaces. The numerical experiments show that the proposed upwinding schemes perform very well.
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