A pressure equation for weakly compressible SPH

2021 ◽  
pp. 105093
Author(s):  
Kalale Chola ◽  
Tsumoru Shintake
Keyword(s):  
Pressure Equation ◽  
Weakly Compressible

scholarly journals Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling

2020 ◽  
Vol 476 (2241) ◽  
pp. 20190801
Author(s):  
Steven J. Lind ◽  
Benedict D. Rogers ◽  
Peter K. Stansby
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Graphics Processing Units ◽  
Wave Structure ◽  
Free Form ◽  
Mesh Free ◽  
Weakly Compressible ◽  
Particle Hydrodynamics ◽  
Massively Parallel Computing ◽  
Smoothed Particle ◽  
Graphics Processing

This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.

A Generalized Compositional Approach for Reservoir Simulation

1983 ◽  
Vol 23 (05) ◽  
pp. 727-742 ◽  
Author(s):  
Larry C. Young ◽  
Robert E. Stephenson
Keyword(s):  
Enhanced Recovery ◽  
Gas Condensate ◽  
Reservoir Modeling ◽  
Pressure Equation ◽  
Compositional Modeling ◽  
Fluid Property ◽  
Black Oil ◽  
Fluid Properties ◽  
Newton Raphson ◽  
Raphson Method

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

scholarly journals Magnetized decaying turbulence in the weakly compressible Taylor-Green vortex

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Forrest W. Glines ◽  
Philipp Grete ◽  
Brian W. O'Shea
Keyword(s):  
Weakly Compressible ◽  
Decaying Turbulence

v-p material point method for weakly compressible problems

2018 ◽  
Vol 176 ◽  
pp. 170-181 ◽  
Author(s):  
Zhen-Peng Chen ◽  
Xiong Zhang ◽  
Kam Yim Sze ◽  
Lei Kan ◽  
Xin-Ming Qiu
Keyword(s):  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Weakly Compressible

Numerical study of jet flow generated by impact on weakly compressible liquid

2006 ◽  
Vol 18 (3) ◽  
pp. 032108 ◽  
Author(s):  
Alexander A. Korobkin ◽  
Alessandro Iafrati
Keyword(s):  
Numerical Study ◽  
Jet Flow ◽  
Compressible Liquid ◽  
Weakly Compressible

scholarly journals A Solution to Pressure Equation with Its Boundary Condition of Combining Tangential and Normal Pressure Relations

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1507
Author(s):  
Hui Xiao ◽  
Wei Liu
Keyword(s):  
Boundary Condition ◽  
Numerical Algorithm ◽  
Iteration Process ◽  
Normal Pressure ◽  
Constitutive Law ◽  
Navier Stokes ◽  
Numerical Verification ◽  
Pressure Equation ◽  
Navier Stokes Equation ◽  
Pressure Boundary Condition

Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without heat and mass transfer. In this paper, a numerical algorithm was proposed to solve this pressure equation by coupling with the Navier-Stokes equation. To match the pressure equation, a method of dealing with pressure boundary condition was presented by combining the tangential and normal direction pressure relations, which should be updated dynamically in the iteration process. Then, a solution to this pressure equation was obtained to bridge the gap between the mathematical model and a practical numerical algorithm. Through numerical verification in a circular tube, it is found that the proposed boundary conditions are applicable. The results demonstrate that the present pressure equation well describes the transport characteristics of the fluid.

A Numerical Investigation Into the Impact Pressures of Different Base Forms Using SPH Method

2014 ◽  
Author(s):  
Zhen Chen ◽  
Li Zou ◽  
Zhi Zong
Keyword(s):  
Free Surface Flows ◽  
Solid Boundary ◽  
Sph Method ◽  
Strong Discontinuities ◽  
Weakly Compressible ◽  
Base Form ◽  
Boundary Treatment ◽  
Sph Model ◽  
Dam Breaking ◽  
The Impact

In this paper, the impact pressures of two different base forms are comparatively studied using Smoothed Particle Hydrodynamics (SPH) method. It is summarized from previous works that the improved weakly compressible SPH model shows better performances than incompressible SPH model in numerical simulations of free surface flows accompany with large deformations and strong discontinuities. Such advantages are observed in numerical accuracy, stability and efficiency. The weakly compressible SPH model used in this paper is equipped with some new correction algorithms, among which include the density reinitialization algorithm and a new coupled dynamic Solid Boundary Treatment (SBT) on solid boundaries. The new boundary treatment combines the advantages of both the repulsive boundary treatment and the dynamic boundary treatment, intending to obtain more stable and accurate numerical results. A benchmark test of dam breaking is conducted to prove the reliability of the numerical model used in this paper. Two representative cases, among which one has one cavity and the other one has three cavities, are numerically investigated and compared to support the conclusion that the base form with cavities generally experience lower local and overall impact pressures than the base form of flat plate. It is found that with the application of cavities on the bottom, the peak values of the boundary pressure near central bottom significantly decrease, leading to smaller force load and better structural stability. The mechanisms of such phenomenon might be the pressure absorption effect conducted by the cavities.

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