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— In this paper we discuss the basic components of the computational technology for the simulation of complex hydrodynamic events, such as a break of a dam, a wave pileup, a landslide, or a mud flow. The technology uses three-dimensional equations of fluid dynamics with free boundaries. The mathematical model is based on the Navier–Stokes equations with… (More)

The paper introduces a finite difference solver for the unsteady incompressible Navier-Stokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the… (More)

In this paper we study a numerical method for the simulation of free surface flows of viscoplastic (Herschel-Bulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. A… (More)

The paper studies a method for numerical simulation of free surface flows of viscous incompressible fluids. The approach is based on the level set method for capturing free surface evolution and features compact finite difference approximations of fluid and level set equations on locally refined and dynamically adapted octree cartesian grids. We consider in… (More)

- Kirill D. Nikitin, Maxim A. Olshanskii, Kirill M. Terekhov, Yuri V. Vassilevski
- Comput. Meth. in Appl. Math.
- 2015

The paper studies a splitting method for the numerical time-integration of the system of partial differential equations describing the motion of viscous incompressible fluid with free boundary subject to surface tension forces. The method splits one time step into a semi-Lagrangian treatment of the surface advection and fluid inertia, an implicit update of… (More)

- K. M. Terekhov, K. D. Nikitin, M. A. Olshanskii, Y. V. Vassilevski
- 2015

We study a numerical method for the simulation of free surface flows of viscoplastic (Herschel-Bulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. We consider an… (More)

The paper introduces a finite difference solver for the unsteady incompressible Navier-Stokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the… (More)

The prediction of large-scale hydrodynamic events such as tsunami spread and run-up, dam break, flood, or landslide run-out is a challenging and important problem of applied mathematics and scientific computing. The paper presents a computational approach based on free surface flow models for fluids of complex rheology to simulate such events and phenomena… (More)