On Lagrangian Meshless Methods in Free-Surface Flows

Abstract

Classically, fluid dynamics have been dealt with analytically because of the lack of numerical resources (Yeung, 1982). With the development of computational ability, many formulations have been developed which typically use the traditional Navier-Stokes equations along with an Eulerian grid. Today, there exists the possibility of using a moving grid (Lagrangian) along with a meshless discretization. The first issue in meshless fluid dynamics is the equations of motion. There are currently two types of Lagrangian formulations. Spherical Particle Hydrodynamics (SPH) is a method which calculates all equations of motion explicitly. The Moving Particle Semi-implicit (MPS) method uses a mathematical foundation based on SPH. However, instead of calculating all laws of motion explicitly, a fractional time step is performed to calculate pressure. A proposed method, Lagrange Implicit Fraction Step (LIFS), has been created which improves the mathematical formulations on the fluid domain. The LIFS method returns to Continuum mechanics to construct the laws of motion based on decomposing all forces of a volume. It is assumed that all forces on this volume can be linearly superposed to calculate the accelerations of each mass. The LIFS method calculates pressure from a boundary value problem with the inclusion of proper flux boundary conditions. The second issue in meshless Lagrangian dynamics is the calculation of derivatives across a domain. The Monte Carlo Integration (MCI) method uses weighted averages to calculate operators. However, the MCI method can be very inaccurate, and is not suitable for sparse grids. The Radial Basis Function (RBF) method is introduced and studied as a possibility to calculate meshless operators. The RBF method involves a solution of a system of equations to calculate interpolants. Machine expenses are shown to limit the viability of the RBF method for large domains.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2005
Accession Number
ADA473689

Entities

People

  • Jon P. Silverberg

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of Motion
  • Fluid Dynamics
  • Hydrodynamics
  • Linear Momentum
  • Mechanics
  • Monte Carlo Method
  • Navier Stokes Equations
  • Partial Differential Equations
  • Pressure Distribution
  • United States Naval Academy

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)