Contributed Talk
Essentially nonoscillatory numerical schemes for implicit methods with large time steps
Slovak University Of Technology, Slovakia
Abstract
Implicit time discretization used in numerical schemes for fully implicit, semi-implicit or IMEX methods
can give an advantage of unconditionally stable behavior of numerical solutions for any choice of time steps.
Although this ensures that no blow up occurs during computations, to ensure essentially non-oscillatory
behavior of numerical solutions, additional limiting of implicit time discretization must be done for larger
time steps that is not necessary for explicit schemes. We present such techniques for high-resolution
unconditionally stable compact implicit numerical schemes for nonlinear conservation laws [1-2]
and nonlinear level set methods [3] and compare them with other approaches.
References
[1] Frolkovič, P., Žeravý, M. (2023). High resolution compact implicit numerical scheme for conservation laws. Applied Mathematics and Computation, 442, 127720.
[2] Žáková, D., Frolkovič, P. (2024). Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes. arXiv preprint arXiv:2407.05275.
[3] Frolkovič, P., Gajdošová, N. (2024). Unconditionally stable higher order semi-implicit level set method for advection equations. Applied Mathematics and Computation, 466, 128460.