scholarly journals Domain Decomposition Modified with Characteristic Mixed Finite Element and Numerical Analysis for Three-Dimensional Slightly Compressible Oil-Water Seepage Displacement

2017 ◽  
Vol 9 (1) ◽  
pp. 143
Author(s):  
Yirang Yuan ◽  
Luo Chang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Optimal Error Estimate ◽  
Computational Domain ◽  
Time Step ◽  
Slightly Compressible ◽  
The Method Of Characteristics

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known problem.

Development of a Three-Dimensional Iterative Methodology Using a Commercial CFD Code for Flow Scouring Around Bridge Piers

2012 ◽  
Author(s):  
Phani Ganesh Elapolu ◽  
Pradip Majumdar ◽  
Steven A. Lottes ◽  
Milivoje Kostic
Keyword(s):  
Shear Stress ◽  
Three Dimensional ◽  
Critical Shear Stress ◽  
Shear Stresses ◽  
Computational Domain ◽  
Time Step ◽  
Mesh Morphing ◽  
River Bed ◽  
Scour Hole ◽  
The Stability

One of the major concerns affecting the safety of bridges with foundation supports in river-beds is the scouring of river-bed material from bridge supports during floods. Scour is the engineering term for the erosion caused by water around bridge elements such as piers, monopiles, or abutments. Scour holes around a monopile can jeopardize the stability of the whole structure and will require deeper piling or local armoring of the river-bed. About 500,000 bridges in the National Bridge Registry are over waterways. Many of these are considered as vulnerable to scour, about five percent are classified as scour critical, and over the last 30 years bridge failures caused by foundation scour have averaged about one every two weeks. Therefore it is of great importance to predict the correct scour development for a given bridge and flood conditions. Apart from saving time and money, integrity of bridges are important in ensuring public safety. Recent advances in computing boundary motion in combination with mesh morphing to maintain mesh quality in computational fluid dynamic analysis can be applied to predict the scour hole development, analyze the local scour phenomenon, and predict the scour hole shape and size around a pier. The main objective of the present study was to develop and implement a three dimensional iterative procedure to predict the scour hole formation around a cylindrical pier using the mesh morphing capabilities in the STARCCM+ commercial CFD code. A computational methodology has been developed using Python and Java Macros and implemented using a Bash script on a LINUX high performance computer cluster. An implicit unsteady approach was used to obtain the bed shear stresses. The mesh was iteratively deformed towards the equilibrium scour position based on the excess shear stress above the critical shear stress (supercritical shear stress). The model solves the flow field using Reynolds Averaged Navier-Stokes (RANS) equations, and the standard k–ε turbulence model. The iterative process involves stretching (morphing) a meshed domain after every time step, away from the bottom where scouring flow parameters are supercritical, and remeshing the relevant computational domain after a certain number of time steps when the morphed mesh compromises the stability of further simulation. The simulation model was validated by comparing results with limited experimental data available in the literature.

Sign in / Sign up

Export Citation Format

Share Document