Journal of Computational Physics
Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation
Journal of Computational Physics
Exponential time differencing for stiff systems
Journal of Computational Physics
Journal of Computational Physics
Short note: a convexity preserving scheme for conservative advection transport
Journal of Computational Physics
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Hi-index | 31.45 |
Toward the unified simulation of the large deformation of a rigid viscoelastic material (plate) and the convection of a viscous fluid (mantle), an Eulerian scheme with a semi-Lagrangian method is developed. The scheme adopts the CIP-CSLR method for advection terms of staggered grid system in three dimensions. The positive transported profile of a positive quantity is assured by flux corrections in the dimensional splitting method. The Jaumann co-rotational effect of the stress tensor is also integrated into the semi-Lagrangian treatment. This co-rotated semi-Lagrangian method is combined with an exponential time differencing method in the time development of the Maxwell constitutive model. The large time step comparable to, or larger than, the Maxwell relaxation time is successfully realized. Validation tests are performed for the three-dimensional Rayleigh-Taylor instability of a viscoelastic material with jump discontinuity of the mass density and other material properties.