Instability in Leapfrog and Forward-Backward Schemes, Part II-Numerical Simulations of Dam Break
Following Sun’s approach , Shuman smoothing instead of conventional diffusion terms is used in a simple two-time step semi-implicit finite volume scheme to simulate dam break. When the Courant number is less than one, the absolute value of amplification factor of the 1D linearized shallow-water equations is 1 in this new scheme. Compared with the characteristic-based semi-Lagrangian schemes and the Riemann solver, this scheme produces excellent results of free water depth and speed of the shock. Numerical simulations show that the water inside the dam initially moves away radially until water almost depletes near the center; then the water moves back to the center and forms a vertical water column there. This paper proves that Shuman smoothing can be used not only in the linearized shallow-water equations discussed in Sun  but also in the nonlinear wave equations to control instability around shocks.
Riemann solver, shallow-water eqyatuibsm senu-implicit scheme, Eigenvalue, characteristic-base, semi-Lagranian, shock
Date of this Version
Sun, Wen Yih, "Instability in Leapfrog and Forward-Backward Schemes, Part II-Numerical Simulations of Dam Break" (2010). Department of Earth, Atmospheric, and Planetary Sciences Faculty Publications. Paper 84.
Link Out to Full Text