Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives

Smith

et al. 2017

Preprint

Abstract:Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

Section: D Sound Propagation In Unsteady Flowsupporting

confidence: 91%

A Lagrangian Approach for Computational Acoustics with Meshfree Method

Smith

et al. 2017

Preprint

J. Ocean Eng. Mar. Energy

“…This Laplacian discretization is named as corrective smoothed particle method (CSPM) following Schwaiger (2008). Fatehi and Manzari (2011) derived a new scheme (they called it as Scheme 4) using error analysis. Careful examination reveals that their new scheme is almost the same as the CSPM.…”

Section: Lp-sph07mentioning

confidence: 99%

“…(20) is accurately estimated. Therefore, the scheme by Fatehi and Manzari (2011) may be considered as one with the similar accuracy as CSPM. As indicated by Chen et al (1999), the solution of the equation theoretically gives the exact value of the second derivatives for any particle distribution if the pressure is a constant, linear or parabolic field and if p ,α (x i ) equals the exact value of the first derivatives of the pressure.…”

Section: Lp-sph07mentioning

confidence: 99%

A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves

Zhou

Yan

2016

Three meshless methods, including incompressible smooth particle hydrodynamic (ISPH), moving particle semi-implicit (MPS) and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R) methods, are often employed to model nonlinear or violent water waves and their interaction with marine structures. They are all based on the projection procedure, in which solving Poisson's equation about pressure at each time step is a major task. There are three different approaches to solving Poisson's equation, i.e. (1) discretizing Laplacian directly by approximating the second-order derivatives, (2) transferring Poisson's equation into a weak form containing only gradient of pressure and (3) transferring Poisson's equation into a weak form that does not contain any derivatives of functions to be solved. The first approach is often adopted in ISPH and MPS, while the third one is implemented by the MLPG_R method. This paper attempts to review the most popular, though not all, approaches available in literature for solving the equation.

“…3. The convergence with increasing particle resolution in a disturbed system is only guaranteed with higher-order methods (Fatehi and Manzari 2011;Tartakovsky et al 2015).…”

Section: The Simulations Are Performed With Open Boundaries This Meamentioning

confidence: 99%

Study of Multi-phase Flow in Porous Media: Comparison of SPH Simulations with Micro-model Experiments

et al. 2015

We present simulations and experiments of drainage processes in a micro-model. A direct numerical simulation is introduced which is capable of describing wetting phenomena on the pore scale. A numerical smoothed particle hydrodynamics model was developed and used to simulate the two-phase flow of immiscible fluids. The experiments were performed in a micro-model which allows the visualization of interface propagation in detail. We compare the experiments and simulations of a quasistatic drainage process and pure dynamic drainage processes. For both, simulation and experiment, the interfacial area and the pressure at the inflow and outflow are tracked. The capillary pressure during the dynamic drainage process was determined by image analysis.