Method for taking into account gravity in free-surface flow simulation

Riemann solvers and pressure gradients in Godunov-type schemes for variable density incompressible flows

“…Using a standard limiter to reconstruct pressure can result in an imbalance of forces at the free surface and, in turn, either parasitic velocities [21,22,23] or compression at what should be the incompressible limit. Only Qian et al [17] have addressed this problem for the variable-density artificial-compressibility equations, and only in the hydrostatic case.…”

“…It is the free surface that complicates matters. The jump in density leads to a jump in ∇p which, if not calculated carefully, can lead to spurious or parasitic velocities [21,22,23]. In a Godunov-type scheme, the problem arises because the gradients calculated in the MUSCL reconstruction step indiscriminately include information from both sides of the free surface.…”

“…Without special treatment, standard MUSCL reconstruction will not account for the impact of a density discontinuity on the pressure gradient. This can result in an imbalance of forces at the free surface and, in turn, either parasitic velocities [21,22,23] or erroneous compression at what should be the incompressible limit. As will be shown later, the compression can resemble Gibbs-type oscillations, but it is a distinct problem of its own that persists even with the most severe of limiters.…”

Technology of 3D Simulation of High-Speed Damping Processes in the Hydraulic Brake Device

“…Discretization of the convective terms in the equation of motion, equation of transfer of turbulent parameters, is performed by the upwind scheme LUD [10], and in the volume fraction transfer equation, by the HRIC scheme [1], which prevents excessive numerical diffusion of the phase interface. The force of gravity was included using a bulk force fitting algorithm [14].…”

“…LOGOS is a 3D multi-physics code for convective heat and mass transfer, aerodynamic and hydrodynamic simulations on parallel computers [11,[13][14][15][16][17][18]. LOGOS has been successfully verified and demonstrated with sufficiently high efficiency on a number of various hydrodynamic tests, including propagation of gravity waves on a free surface (tsunami) [2,14,18] and industry-specific simulations [11,15]. Speedup of computations on highly parallel computers is provided by an original implementation of the algebraic multigrid method [11,19].…”