Our aims are to demonstrate the effectiveness of multiscale simulations for slide generated tsunamis. Finally, we show the effect of incorporating palaeobathymetric changes on the simulated run-up heights. Fluidity is a highly flexible finite-element/control-volume modelling framework which allows for the numerical solution of a number of equation sets (Piggott et al., 2008) and has been used in a number of

flow studies ranging from laboratory- to ocean-scale (e.g. Wells et al., 2010, Hill et al., 2012 and Hiester et al., 2011). In an ocean modelling context, Fluidity has been used to model both modern and ancient earthquake-generated tsunamis (Oishi et al., 2013, Mitchell et al., 2010 and Shaw et al., 2008). Here, Fluidity is used to solve the non-hydrostatic incompressible Navier–Stokes equations under the Boussinesq approximation in a rotating reference frame: equation(1a) ∂u∂t+u·∇u+2Ω×u=-∇pρ+∇·ν∇u-gk, buy Vemurafenib equation(1b) ∇·u=0,∇·u=0,where uu is the 3D velocity vector, t   represents time, p   is pressure, νν is the kinematic viscosity tensor (isotropic and set to 1 m2 s−1) and ρρ denotes the density, which is constant in this work. The reason for choosing an isotropic viscosity is

that experiments showed no discernible differences in results when using different values of viscosity in the horizontal and vertical when using a single layer of elements. This may not be www.selleckchem.com/products/byl719.html the case when multiple layers are used to capture dispersion ( Oishi et al., 2013). ΩΩ is the rotational velocity

of the Earth and g   is the gravitational Urocanase acceleration with kk pointing in the radial, upward direction. Eq. (1a) is discretised using a linear discontinuous Galerkin approximation (P1DGP1DG) for velocity. A pressure projection method is used to solve for the pressure p   and enforce a divergence-free velocity field at the end of each time-step. Pressure is discretised using a continuous Galerkin, piecewise quadratic formulation (P2). The resulting P1DGP2P1DGP2 velocity/pressure discretisation has a number of desirable properties described fully in Cotter et al., 2009a and Cotter et al., 2009b and Cotter and Ham (2011). A two-level θθ method is employed for time-integration. Here θ=0.5θ=0.5 which yields a second-order accurate, implicit Crank–Nicolson scheme. Two Picard iterations per time-step are used to linearise the nonlinear advection term. A combined pressure-free-surface kinematic boundary condition formulation is employed as the top boundary condition (Funke et al., 2011 and Oishi et al., 2013). A no-normal flow with a quadratic bottom drag, with dimensionless coefficient CDCD set to 0.0025, is applied at the bottom, except where the slide motion is prescribed (see Section 2.2). At the coastlines a free-slip no-normal flow formulation is used and at the open boundaries either a velocity or a free surface elevation is prescribed.