Nonreflecting Outlet Boundary Conditions
for Smoothed Particle Hydrodynamics
Simulation of Small-Scale Open-Channel Flow
Thanh T. Bui (B) and Susumu Nakata
Ritsumeikan University, Shiga 525-8577, Japan
gr0399rr@ed.ritsumei.ac.jp
Abstract. In this paper, we propose a nonreflecting outlet boundary condition
(NROBC) for particle-based fluid simulation as a combination of inflow/outflow
algorithm and periodic boundary condition. We assume to use δ-SPH scheme
for weakly compressible flows. In the inflow/outflow algorithm, the domain is
divided into four zones: fluid, wall, inflow and outflow zones. The NROBC proposed in this paper inherits the advantage of the periodic boundary condition in
the sense that the number of particles is constant. This property contributes to
conservation of total mass and insertion of inflow particles without rearranging
process. The physical quantities such as density and velocity at the inflow zone
are unknown depending on the situation. Our boundary condition supports both
cases, prescribed and non-prescribed, and the loss of the accuracy is small even
if the quantities are non-prescribed at the inflow zone. In addition, tensile instability is effectively reduced by particle shifting technique. Several simulations are
presented to validate and demonstrate the applicability and versatility of the proposed technique. Comparisons between numerical results and analytical solutions
are provided with very low Mean Square Error Percent (MSEP) in both test cases.
Keywords: Fluid simulation · SPH · Open boundary · Periodic boundary
condition
1 Introduction
Open boundary conditions are difficult to implement in smoothed particle hydrodynamics (SPH) method. A number of investigation about this issue has been previously
addressed by different authors.
In many SPH simulations, periodic boundary conditions are employed [1, 2], where
the particle distribution is continually recycled so that the particles pass through the
outlet, it is vice versa at the inlet. The drawbacks of this technique are the violation by
the outlet velocity field after re-inserted.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 60–71, 2021.
https://doi.org/10.1007/978-3-030-64690-5_7
for Smoothed Particle Hydrodynamics
Simulation of Small-Scale Open-Channel Flow
Thanh T. Bui (B) and Susumu Nakata
Ritsumeikan University, Shiga 525-8577, Japan
gr0399rr@ed.ritsumei.ac.jp
Abstract. In this paper, we propose a nonreflecting outlet boundary condition
(NROBC) for particle-based fluid simulation as a combination of inflow/outflow
algorithm and periodic boundary condition. We assume to use δ-SPH scheme
for weakly compressible flows. In the inflow/outflow algorithm, the domain is
divided into four zones: fluid, wall, inflow and outflow zones. The NROBC proposed in this paper inherits the advantage of the periodic boundary condition in
the sense that the number of particles is constant. This property contributes to
conservation of total mass and insertion of inflow particles without rearranging
process. The physical quantities such as density and velocity at the inflow zone
are unknown depending on the situation. Our boundary condition supports both
cases, prescribed and non-prescribed, and the loss of the accuracy is small even
if the quantities are non-prescribed at the inflow zone. In addition, tensile instability is effectively reduced by particle shifting technique. Several simulations are
presented to validate and demonstrate the applicability and versatility of the proposed technique. Comparisons between numerical results and analytical solutions
are provided with very low Mean Square Error Percent (MSEP) in both test cases.
Keywords: Fluid simulation · SPH · Open boundary · Periodic boundary
condition
1 Introduction
Open boundary conditions are difficult to implement in smoothed particle hydrodynamics (SPH) method. A number of investigation about this issue has been previously
addressed by different authors.
In many SPH simulations, periodic boundary conditions are employed [1, 2], where
the particle distribution is continually recycled so that the particles pass through the
outlet, it is vice versa at the inlet. The drawbacks of this technique are the violation by
the outlet velocity field after re-inserted.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 60–71, 2021.
https://doi.org/10.1007/978-3-030-64690-5_7