Corrective Smoothed Particle Method Research Articles

Heat Transfer Analysis for FGMs Using SPH-CSPM

The solution of heat transfer problems for functional graded materials (FGMs) by smoothed particle hydrodynamics, in which the thermal conductivity is a function of the spatial coordinates and the temperature, is discussed for both steady and non-steady problems under various boundary conditions. The boundary is treated using the corrective smoothed particle method to heighten the accuracy. Several calculations are performed to test the validity of the formulation. As an example of practical application, the problem of FGM cylindrical plates subjected to thermal shock is calculated, in which the thermal conductivity is temperature dependent and the heat transfer coefficient is varied in radial direction.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.

Unsteady fluid–solid interaction by a kernel‐based particle method

AbstractA Lagrangian stabilized particle method is adopted for the simulation of unsteady fluid flow and gas dynamics. The velocity field smoothing technique, which was successfully implemented for reducing zero energy modes and tensile instabilities in solid problems, is used for the stabilization of the fluid phase. In this method a smoothing technique has been applied and the field values in particles are prevented from excessive jumps due to instability. This approach can replace traditional stabilization methods such as the artificial viscosity approach. In this paper, the corrective smoothed particle method has been implemented for solving governing partial differential equations of fluid. Also a modification in basic governing equations is performed on boundary interfaces to conserve mass and energy quantities. The method is implemented and verified in one‐ and two‐dimensional compressible flow problems. Copyright © 2009 John Wiley & Sons, Ltd.

A one-dimensional meshfree particle formulation for simulating shock waves

In this paper, a one-dimensional meshfree particle formulation is proposed for simulating shock waves, which are associated with discontinuous phenomena. This new formulation is based on Taylor series expansion in the piecewise continuous regions on both sides of a discontinuity. The new formulation inherits the meshfree Lagrangian and particle nature of SPH, and is a natural extension and improvement on the traditional SPH method and the recently proposed corrective smoothed particle method (CSPM). The formulation is consistent even in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in CSPM, and a corrective part derived from the discontinuity. A numerical study is carried out to examine the performance of the formulation. The results show that the new formulation not only remedies the boundary deficiency problem but also simulates the discontinuity well. The formulation is applied to simulate the shock tube problem and a 1-D TNT slab detonation. It is found that the proposed formulation captures the shock wave at comparatively lower particle resolution. These preliminary numerical tests suggest that the new meshfree particle formulation is attractive in simulating hydrodynamic problems with discontinuities such as shocks waves.

A corrective smoothed particle method for transient elastoplastic dynamics

An incremental approach is presented to model transient, elastoplastic dynamic problems using the corrective smoothed particle method. It uses the corrective first- and second-derivative approximations to solve the nonlinear momentum equations, which is described in terms of displacement increments entirely. This algorithm not only satisfies the nodal completeness condition but also exhibits no integrablity problem. Several 2D examples, including forced vibration, stress wave propagation, and rigid wall impact, are investigated to demonstrate the numerical stability and accuracy of the proposed method.

Completeness of corrective smoothed particle method for linear elastodynamics

Two different solution algorithms of the corrective smoothed particle method (CSPM) are developed and examined with linear elastodynamic problems. One is to use the corrective first derivative approximations to solve the stress-based momentum equations, with stresses evaluated from the strains. This is an approach that has widely been adopted in smoothed particle hydrodynamics (SPH) methods. The other is new, in which the corrective second derivative approximations are used to directly solve the displacement-based Navier equations. The former satisfies the nodal completeness condition but lacks integrability; on the contrary, the latter is truly complete. Numerical tests show that the latter outperforms the former as well as other existing SPH methods, as expected.

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

Combining the kernel estimate with the Taylor series expansion is proposed to develop a Corrective Smoothed Particle Method (CSPM). This algorithm resolves the general problem of particle deficiency at boundaries, which is a shortcoming in Standard Smoothed Particle Hydrodynamics (SSPH). In addition, the method’s ability to model derivatives of any order could make it applicable for any time-dependent boundary value problems. An example of the applications studied in this paper is unsteady heat conduction, which is governed by second-order derivatives. Numerical results demonstrate that besides the capability of directly imposing boundary conditions, the present method enhances the solution accuracy not only near or on the boundary but also inside the domain. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. government work and is in the public domain in the United States.

An improvement for tensile instability in smoothed particle hydrodynamics

A corrective Smoothed-Particle Method (CSPM) is proposed to address the tensile instability and, boundary deficiency problems that have hampered full exploitation of standard smoothed particle hydrodynamics (SPH). The results from applying this algorithm to the 1-D bar and 2-D plane stress problems are promising. In addition to the advantage of being a gridless Lagrangian approach, improving the above two major obstacles in standard SPH makes it attractive for applications in computational mechanics.