Reformulation of Smoothed Particle Hydrodynamics with Riemann Solver

By S. Inutsuka. 2002

209 citations recorded by the source corpus.

Smoothed particle hydrodynamics is reformulated in terms of the convolution of the original hydrodynamics equations, and the new evolution equations for the particles are derived. The same evolution equation of motion is also derived using a new action principle. The force acting on each particle is determined by solving the Riemann problem. The use of the Riemann solver strengthens the method, making it accurate for the study of phenomena with strong shocks. The prescription for the variable smoothing length is shown. These techniques are implemented in strict conservation form. The results of a few test problems are also shown.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/d5d0db4db72e4b9caae45b4640db642ab9f1c3ac

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In Computational Mechanics

Citations in the corpus

Moving mesh cosmology: the hydrodynamics of galaxy formation (2011, methodology): “…of mixing in SPH by modifying the standard set of discretized equations (see e.g. Price 2008; Wadsley, Veeravalli & Couchman 2008; Heß & Springel 2010) or by incorporating a Riemann solver in place of the artificial viscosity (e.g. Inutsuka 2002; Cha & Whitworth 2003; Murante et al. 2011).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “…that the uncertain and poorly-defined artificial diffusion operators can be eliminated by appropriate solution of a Riemann problem between particle faces; this has generally appeared in the form of so-called “Godunov SPH” (Cha & Whitworth 2003; Inutsuka 2002; Cha et al. 2010; Murante et al. 2011).”
Comparison study of MPM and SPH in modeling hypervelocity impact problems (2009, methodology): “Monaghan [55] and Inutsuka [56] improve the SPH shock simulation by introducing Riemann solver.”
Astrophysical smooth particle hydrodynamics (2009, background): “…starting point one may want to consult (Steinmetz and Müeller, 1994, 1995; Raiteri et al., 1996; Carraro et al., 1998; Berczik, 1999; Kawata and Gibson, 2003; Kobayashi, 2004; Tornatore et al., 2004; Scannapieco et al., 2005; Martinez-Serrano et al., 2008; Greif et al., 2009; Wiersma et al., 2009).”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, unknown): “[15,45].”
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH (2007, methodology): “…a numerical simulation is a somewhat meaningless quantity (since the real shock width is many orders of magnitude smaller than the resolution length of any numerical code), recent efforts (Inutsuka, 2002; Cha and Whitworth, 2003) have shown that such methods can also be utilised in an SPH context.”
Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future (2016, methodology): “Its attraction for SPH was quickly realized in some early publications (Monaghan 1997), but it was not until the near simultaneous work of Inutsuka (2002), Cha and Whitworth (2003), Parshikov and Medin (2002), and Vila (1999) that a more formal development of shock-capturing techniques within SPH wa”
A multi-phase SPH method for macroscopic and mesoscopic flows (2006, methodology): “For instance, Inutsuka (2002) solves a Riemann problem to obtain the inter-particle average state.”
Moving mesh cosmology: numerical techniques and global statistics (2011, methodology): “For example, the artificial viscosity typically used in SPH codes to handle shocks could, in principle, be eliminated by incorporating a Riemann solver into SPH. Pioneering efforts along these lines have been made by Inutsuka (2002) and Murante et al. (2011).”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, methodology): “In the context of weakly compressible SPH, the so-called delta-SPH (Antuono et al. 2012) as well as Riemann SPH (Inutsuka 1994, 2002; Monaghan 1997; Gao et al. 2012; Rafiee et al. 2012) schemes have been proposed to enhance the accuracy, especially in terms of reproduced pressure field.”