Improved procedure for the computation of Lamb’s coefficients in the physalis method for particle simulation

Abstract

a b s t r a c tThe PHYSALIS method was designed for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finitedifference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solution with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. A novel test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle.

Rotational dynamics of a particle in a turbulent stream

“…To gain some insight into the relative importance of the two mechanisms we can study the magnitude of the forces Eq. (20). By nondimensionalizing them according to Eq.…”

“…in which I is the particle moment of inertia and is the particle angular velocity. The method, which has been extensively validated in earlier papers [see, e.g., 20,21], is accurate and efficient. Since the Lamb solution is expressed as a series of spherical harmonics, the error decreases exponentially, rather than algebraically, as the number of degrees of freedom used to describe each particle is increased.…”

“…A point to stress is that the numerical method used in this work is singularly appropriate for this problem as it leads to a very accurate evaluation of the hydrodynamic torque on the particle, as documented in Ref. [20].…”

GPU-centric resolved-particle disperse two-phase flow simulation using the Physalis method

“…Prosperetti [23], Zhang and Prosperetti [30], Gudmundsson and Prosperetti [11] to provide a more detailed description. The flow solution procedure at each point in time generally proceeds as follows.…”

“…Due to the no-slip boundary condition at the surface of each particle, Lamb's solution increases in accuracy as the distance from the surface decreases. We solve the Navier-Stokes equations (1) according to these boundary conditions (2) and check that the two solutions match at their interface by calculating Lamb's coefficients based on the most recent flow information using the scalar product method posed in Gudmundsson and Prosperetti [11], which takes the form of spherical surface integration,…”