implicit method

Mesh-free particle (Lagrangian) methods، such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH)، are the newest methods in computational fluid dynamics، which have been applied in flow problems with large deformations and inconsistency. The aim of ths research was to develop and improve the simulation of free surface flows، using the new method of weakly compressible MPS (WC-MPS). In the MPS method، pressure is determined by solving Poisson equation. This equation is solved implicitly، which needs too much computer time. In the present research، the WC-MPS method is used to calculate pressure. In this method، as in SPH method، the state equation is used. This equation is solved explicitly، which does not occupy too much computer time. To evaluate the proposed method، the famous applied flow problem of dam break is analyzed. The program is written in C language and validations are performed for this code. To compare the Lagrangian approach with Eulerian approach، dam break is modeled by using FLOW-3D software too. The results of modeling approaches and physical models showed that both approaches have acceptable accuracy in modeling the free surface flow، but the accuracy of Lagrangian approach، especially the WC-MPS، is more than Eulerian approach. The proposed methos had some pressure oscillations، which were analyzed thereafter. Simulation of free surface flows using Weakly compressible moving-particle semi-implicit methodMesh-free particle (Lagrangian) methods، such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH)، are the newest methods in computational fluid dynamics، which have been applied in flow problems with large deformations and inconsistency. The aim of ths research was to develop and improve the simulation of free surface flows، using the new method of weakly compressible MPS (WC-MPS). In the MPS method، pressure is determined by solving Poisson equation. This equation is solved implicitly، which needs too much computer time. In the present research، the WC-MPS method is used to calculate pressure. In this method، as in SPH method، the state equation is used. This equation is solved explicitly، which does not occupy too much computer time. To evaluate the proposed method، the famous applied flow problem of dam break is analyzed. The program is written in C language and validations are performed for this code. To compare the Lagrangian approach with Eulerian approach، dam break is modeled by using FLOW-3D software too. The results of modeling approaches and physical models showed that both approaches have acceptable accuracy in modeling the free surface flow، but the accuracy of Lagrangian approach، especially the WC-MPS، is more than Eulerian approach. The proposed methos had some pressure oscillations، which were analyzed thereafter. Simulation of free surface flows using Weakly compressible moving-particle semi-implicit method

In this paper, an implicit high order discretization has been developed for gridless method. In recent decade, gridless method using a distribution of points has become an important research topic in computational fluid dynamics. Gridless method usually uses the first order Taylor series for discretization of the space derivatives at any points. This paper presents an extension of high order for a central difference gridless method and investigates the results accuracy and performance of this method for solving inviscid compressible flows. Euler equations have been solved in two dimensional using second and fourth order artificial dissipation terms. These terms make a fast gridless method. The method of discretization in time, Explicit and dual-time implicit time discretization are used. In order to reduce the computational cost, local time stepping and residual smoothing techniques are utilized to speed up convergence. The capabilities and accuracy of the method are compared with finite volume method and experimental data for airfoils in transonic and supersonic flows. Results show that the second order accuracy solutions with fewer point distributions indicate higher accuracy when compared to the first order accuracy solutions in transonic and supersonic flows.

Mesh-free particle (Lagrangian) methods, such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH), are the newest methods in computational fluid dynamics, which have been applied in flow problems with large deformations and inconsistency. The aim of this research was to develop and improve the simulation of open-boundary free-surface flows, using the new method of weakly compressible MPS (WC-MPS). Most studies in the field of Lagrangian models are concerned with closed boundary conditions. This study, introduces a comprehensive method for MPS modeling of cases with inflow and outflow boundaries. Inflow and outflow boundaries are considered and the boundary conditions and recycling of particles are prescribed. The algorithm not only improves the inlet and outlet boundary conditions, but also reduces the pressure fluctuations at boundaries. To evaluate the proposed method, the famous applied flow problem of ogee spillway and steady shallow flow over curved bed is analyzed. The program is written in C language and validations are performed for this code. Comparison of the results of proposed model and physical models showed acceptable accuracy in modeling the free surface flows with open boundary conditions.

A consistent implicit Incompressible Smoothed Particle Hydrodynamics (ISPH) method based on projection approach is proposed for solving violent free surface flow problems. In this way، two consistent discretization schemes are employed for first and second spatial derivatives. In this study، it is shown that in explicit ISPH solvers، the field variables and the positions of particles in the process of numerical differentiation are estimated at two different time steps. So، the incompressibility is not completely satisfied. In the present approach، an iteration loop is implemented، in each time-step. Thus، at the end of each time-step both velocity and the positions used in divergence estimation are at the new time-level. The proposed ISPH method is validated in free surface flow problems involving 2-D dam break benchmarks in which both wet and dry beds are considered. Among the advantages of the present implicit method is being more accurate and stable than the explicit one، despite use of lower number of particles and greater time-step sizes. Also، it provides significant improvement in free surface simulations and pressure distribution results.

In this paper, time domain dynamic analysis of dam-reservoir interaction is presented using finite difference method. A semi-implicit scheme is used for the discretization of the governing equation of dam, and an explicit scheme is used for the discretization of the governing equation of fluid. Water is considered compressible but its internal viscosity is neglected. A Sommerfeld’s radiation condition at the infinity boundary of the fluid domain is implemented. To verify the proposed method, numerical examples are given to be compared with the existing solutions. The result shows a good agreement with semi-analytical solution. Finally, the effects of reservoir bottom absorption, the free surface waves of the reservoir and the vertical component of earthquake are analyzed and the results are presented.