10.20381/ruor-6184
Nguyen, Thu Huong
Strong Stability Preserving Hermite-Birkhoff Time Discretization Methods
Université d'Ottawa / University of Ottawa
2012
Strong stability preserving
Hermite-Birkhoff method
SSP coefficient
Time discretization
Method of lines
Université d'Ottawa / University of Ottawa
Université d'Ottawa / University of Ottawa
2012-11-06
2012-11-06
2012
2012
en
Thesis
http://hdl.handle.net/10393/23491
The main goal of the thesis is to construct explicit, s-stage, strong-stability-preserving (SSP) Hermite–Birkhoff (HB) time discretization methods of order p with nonnegative coefficients for the integration of hyperbolic conservation laws. The Shu–Osher form and the canonical Shu–Osher form by means of the vector formulation for SSP Runge–Kutta (RK) methods are extended to SSP HB methods. The SSP coefficients of k-step, s-stage methods of order p, HB(k,s,p), as combinations of k-step methods of order (p − 3) with s-stage explicit RK methods of order 4, and k-step methods of order (p-4) with s-stage explicit RK methods of order 5, respectively, for s = 4, 5,..., 10 and p = 4, 5,..., 12, are constructed and compared with other methods. The good efficiency gains of the new, optimal, SSP HB methods over other SSP methods, such as Huang’s hybrid methods and RK methods, are numerically shown by means of their effective SSP coefficients and largest effective CFL numbers. The formulae of these new, optimal methods are presented in their Shu–Osher form.