The moving-least-squares-particle hydrodynamics method (MLSPH)
- Los Alamos National Lab., NM (United States)
An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for the SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- OSTI ID:
- 332733
- Report Number(s):
- SAND-98-1591; CONF-9709141-PROC.; ON: DE99000778; TRN: IM9916%%35
- Resource Relation:
- Conference: 5. joint Russian-American computational mathematics conference, Albuquerque, NM (United States), 2-5 Sep 1997; Other Information: PBD: [1997]; Related Information: Is Part Of Proceedings of the 5. joint Russian-American computational mathematics conference; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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