Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.

FLOW AROUND A CIRCULAR CYLINDER USING A FINITE-VOLUME TVD SCHEME BASED ON A VECTOR TRANSFORMATION APPROACH

Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solving the Unsteady Reynolds-Averaged Navier-Stokes（URANS） equations.An Elemental Velocity Vector Transformation（EVVT） approach is proposed for the local normal and tangential velocity transformation at the interfaces of main and satellite elements.The presented method is validated by comparing with the available experimental data and numerical results.It is shown that the two-dimensional TVD finite volume method with the Renormalization Group（RNG） turbulence model can be used to determine hydrodynamic forces and captures vortex shedding characteristics very well.

FINITE-VOLUME TVD ALGORITHM FOR DAM-BREAK FLOWS IN OPEN CHANNELS

A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.

Effect of channel shape on selection of time marching scheme in the discontinuous Galerkin method for 1-D open channel flow

One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth （multistep）, and second-order total variation diminishing （TVD） Runge-Kutta （multistage） time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic （rectangular, trapezoidal, triangular, and parabolic cross-sections） and non-prismatic （natural river） channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.

A TVD SCHEME FOR INCOMPRESSIBLE FLOW COUPLED WITH DIFFERENT TURBULENCE MODLES ON A GROUND-MOUNTED SQUARE-RIB FLOW

A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.

A TVD discretization method for shallow water equations:Numerical simulations of tailing dam break

In view of the disastrous consequences of tailings dam break and its unique evolutionary process in complex areas,this paper constructs two-dimensional shallow water equations,rheological equations and mathematical models of tailings sand flows on the basis of Navier–Stokes equations(N–S equations).It performs total variation diminishing(TVD)discretization on these equations,develops forward simulation programs in MATLAB2016 and conducts numerical analyses on three kinds of dam breaks(ideal dam break,asymmetric dam break and dam break with obstacles in the downstream area).The results show that TVD discretization is effective in capturing shock waves.According to the analysis on consequences of Huangmailing Tailings Dam break,the author obtains the maximum distance of tailings sand flow,the flow rate of tailings and the time that tailings reach destinations in the downstream area,thereby providing scientific basis for disaster analyses on similar tailings dam breaks and supplying technical support for emergency rescues after disasters.

Surfactant flooding: The influence of the physical properties on the recovery efficiency

Enhanced Oil Recovery(EOR)processes aim at increasing the performance and operative life of oilfields while newer,greener and more efficient energy sources are developed.Among the chemical EOR techniques,surfactant flooding is one of the most well-known methods,applied mainly in low-and medium-viscosity oilfields.Surfactants diminish the interfacial energy between the oleous and aqueous phases,reducing the forces responsible of the capillary trapping phenomenon and mobilizing the remaining oil.This paper presents the study of a novel two-dimensional surfactant flooding simulator for a four-component(water,petroleum,chemical,salt),two-phase(aqueous,oleous)system in porous media.It is aimed mainly at discussing the influence of the physical phenomena present in the reservoir during the recovery,namely:rock compressibility,diffusion,capillary pressure and adsorption.The system is numerically solved using a second-order finite difference method using the IMPEC(IMplicit Pressure and Explicit Concentration)scheme.The oil recovery factor was negatively affected when these phenomena were considered,being strongly sensitive to the adsorption.The other phenomena decreased the efficiency of the process to a lesser extent,whilst the capillary pressure did not affect significantly the flooding performance.The presence of salt in the reservoir rendered the adsorption process more relevant,with water-in-oil emulsions being more sensitive to the presence of this fourth component.This paper shows the importance of the design and optimization of chemical agents to be used in EOR before its field application.

A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter

The Unsteady Adaptive Stochastic Finite Elements(UASFE)approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations.In this paper,it is shown that the underlying Adaptive Stochastic Finite Elements(ASFE)method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing(ED).It is also shown that the method is total variation diminishing(TVD)for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature.It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time.The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.