CRKSPH - A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme. We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates 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, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. 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 many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the 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.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Bassett, Brody R.; Owen, J. Michael: Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells (2022)
  2. Bassett, Brody R.; Owen, J. Michael; Brunner, Thomas A.: Efficient smoothed particle radiation hydrodynamics. I: Thermal radiative transfer (2021)
  3. Bassett, Brody R.; Owen, J. Michael; Brunner, Thomas A.: Efficient smoothed particle radiation hydrodynamics. II: Radiation hydrodynamics (2021)
  4. Ramachandran, Prabhu; Bhosale, Aditya; Puri, Kunal; Negi, Pawan; Muta, Abhinav; Dinesh, A.; Menon, Dileep; Govind, Rahul; Sanka, Suraj; Sebastian, Amal S.; Sen, Ananyo; Kaushik, Rohan; Kumar, Anshuman; Kurapati, Vikas; Patil, Mrinalgouda; Tavker, Deep; Pandey, Pankaj; Kaushik, Chandrashekhar; Dutt, Arkopal; Agarwal, Arpit: PySPH: a Python-based framework for smoothed particle hydrodynamics (2021)
  5. Rosswog, S.; Diener, P.: SPHINCS_BSSN: a general relativistic smooth particle hydrodynamics code for dynamical spacetimes (2021)
  6. Collé, A.; Limido, J.; Vila, J.-P.: An accurate multi-regime SPH scheme for barotropic flows (2019)
  7. Liu, Xiaoxing; Morita, Koji; Zhang, Shuai: A pairwise-relaxing incompressible smoothed particle hydrodynamics scheme (2019)
  8. Liu, Xiaoxing; Morita, Koji; Zhang, Shuai: An ALE pairwise-relaxing meshless method for compressible flows (2019)
  9. Trask, Nathaniel; You, Huaiqian; Yu, Yue; Parks, Michael L.: An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics (2019)
  10. Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang: Lagrangian particle method for compressible fluid dynamics (2018)
  11. Frontiere, Nicholas; Raskin, Cody D.; Owen, J. Michael: CRKSPH - A conservative reproducing kernel smoothed particle hydrodynamics scheme (2017)
  12. Ha, Cong-Tu; Kim, Dong-Hyun; Park, Warn-Gyu; Jung, Chul-Min: A compressive interface-capturing scheme for computation of compressible multi-fluid flows (2017)