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22 March 2025 |
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CRKSPH - A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme | | Nicholas Frontiere
; Cody D. Raskin
; J. Michael Owen
; | | Date: |
3 May 2016 | | Abstract: | We present a formulation of smoothed particle hydrodynamics (SPH) that
employs a first-order consistent reproducing kernel function, exactly
interpolating linear fields with particle tracers. Previous formulations using
reproducing kernel (RK) interpolation have had difficulties maintaining
conservation of momentum due to the fact the RK kernels are not, in general,
spatially symmetric. Here, we utilize a reformulation of the fluid equations
such that mass, momentum, and energy are all manifestly conserved without any
assumption about kernel symmetries. Additionally, by exploiting the increased
accuracy of the RK method’s gradient, we formulate a simple limiter for the
artificial viscosity that reduces the excess diffusion normally incurred by the
ordinary SPH artificial viscosity. Collectively, we call our suite of
modifications to the traditional SPH scheme Conservative Reproducing Kernel
SPH, or CRKSPH. CRKSPH retains the benefits of traditional SPH methods (such as
preserving Galilean invariance and manifest conservation of mass, momentum, and
energy) while improving many of the well-known shortcomings of SPH,
particularly the overly aggressive artificial viscosity and zeroth-order
inaccuracy. We compare CRKSPH to two different modern SPH formulations
(pressure based SPH and compatibly differenced SPH), demonstrating the
advantages of our new formulation when modeling fluid mixing, strong shock, and
adiabatic phenomena. | | Source: | arXiv, 1605.0725 | | Services: | Forum | Review | PDF | Favorites | |
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