A corrective smoothed particle method for boundary value problems in heat conduction

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: Introductionmentioning

confidence: 99%

A Lagrangian Approach for Computational Acoustics with Meshfree Method

Smith

et al. 2017

Preprint

“…In order to address this problem, several effective techniques, such as the corrective smoothed particle method (CSPM), have been proposed [2]. The finite particle method (FPM) has also been proposed by Liu and Liu [3].…”

Section: Introductionmentioning

confidence: 99%

Study on Particle Inconsistency Problem in Smoothed Particle Hydrodynamics

戎

Kisu

2011

AMM

Abstract. In the smoothed particle hydrodynamics (SPH) method, the particle inconsistency problem significantly influences the calculation accuracy. In the present study, we investigate primarily the influence of the particle inconsistency on the first derivative of field functions and discuss the behavior of several methods of addressing this problem. In addition, we propose a new approach by which to compensate for this problem, especially for functions having a non-zero second derivative, that is less computational demanding, as compared to the finite particle method (FPM). A series of numerical studies have been carried out to verify the performance of the new approach. IntroductionSmoothed particle hydrodynamics (SPH) [1] is a mesh-free or particle-based method for solving physical phenomena expressed by partial differential equations and has been widely used in various spheres. However, SPH has some numerical problems. One of these problems is the particle inconsistency that results from the particle approximation process, which leads to low calculation accuracy. Concretely speaking, because of the particle approximation features of SPH, the particle inconsistency problem associated with boundary particles, irregular distributed particles, or the choice of the smoothing length will occur. An appropriate countermeasure to address this problem is very important, because these cases frequently appear in actual analyses.In order to address this problem, several effective techniques, such as the corrective smoothed particle method (CSPM), have been proposed [2]. The finite particle method (FPM) has also been proposed by Liu and Liu [3]. In their paper, the accuracy of approximating field functions in such cases is investigated using conventional SPH, the CSPM, and the FPM, which is shown to be extremely accurate.However, they discuss only the case for approximating field functions, and only limited a constant field function and a linear field function are investigated. In fact, evaluation of the influence on the accuracy resulting from the particle inconsistency is indispensable not only for a field function but also for derivatives of the field function.From this point of view, we have developed the extended CSPM, which is based on the conventional CSPM, in order to approximate the derivatives of a field function more accurately with a smaller matrix than in the FPM, considering that the calculation in a particle method will be repeated for each particle and each time step. Several calculations in the one-dimensional problem are carried out in order to investigate the effect of the new approach.

Safety and Security Engineering III

“…The authors of [5] proposed the ghost particle method, in which some particles are located outside the domain. The heat conduction problem is solved in [6], where Taylor series expansion approximates the regularization kernels.…”

Section: Introductionmentioning

confidence: 99%

Aftermath of explosions in underground free space

Procházka¹,

Kravtsov²

2009

Today's world has a very urbanized structure -more than half the population of 6,8 billion people live in cities, and underground spaces are one of the most prerogative zones for city's of modern civilization. Underground spaces have grown, along with the risk of terrorism and its organization. Therefore, it is very important to predict the dynamic impacts of explosives in underground spaces and the blast waves can be transformed into a loading of solid structures. In this paper, the impact of explosions and air strike waves is formulated and solved. The location of the center of explosion is very relevant. It appears that if the location is at the solid surface, this part can be up to 30% of the total energy (in soft solids). The variables to be calculated are the mass density of gas, the velocity of movements and the internal energy. The latter covers the influence of the gas pressure, being given for the adiabatic state. The air is linearly related to the internal energy of a unit mass of the gas, as is the density, while in the neighborhood of the source of explosion, the pressure changes nonlinearly with respect to the gas density.