Contributed Talk
Novel high-resolution semi-implicit finite volume methods for conservation laws
Slovak University Of Technology - Slovakia
Abstract
In this talk we present recent results on our development of higher order semi-implicit finite volume methods applied to some representative equations of conservation laws. The method can be seen as an extension of the first order accurate implicit method as given, e.g., in [1]. In its simplest form it is based on a partial Cauchy-Kowalevski (or Lax-Wendroff) procedure when the time derivatives in the Taylor series are replaced by mixed derivatives using the PDE [2]. To suppress nonphysical oscillations in numerical solutions, the TVD second order accurate form is derived similarly to [3].
Moreover, first results on the WENO type of semi-implicit finite volume schemes will be presented.
References
[1] Lozano, E., & Aslam, T. D. (2021). Implicit fast sweeping method for hyperbolic systems of conservation laws. Journal of Computational Physics, 430, 110039.
[2] Frolkovič, P., & Mikula, K. (2018). Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids. Applied Mathematics and Computation, 329, 129-142.
[3] Duraisamy, K., & Baeder, J. D. (2007). Implicit scheme for hyperbolic conservation laws using nonoscillatory reconstruction in space and time. SIAM Journal on Scientific Computing, 29(6), 2607-2620.