A differential quadrature analysis of unsteady open channel flow

Abstract

A rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical simulation of unsteady open channel flow. To the best of authors' knowledge, this is the first attempt to use the DQM in open channel hydraulics. The Saint-Venant equations and the related nonhomogenous, time dependent boundary conditions are discretized in spatial and temporal domain by DQ rules. The unknowns in the entire domain are computed by satisfying governing equations, boundary and initial conditions simultaneously. By employing DQM, accurate results can be obtained using dramatically less grid points in spatial and time domain. The stability of DQM solution is not sensitive to choosing time step or Courant number unlike other methods. Although numerical problems such as instability, oscillation and underestimation near critical depth can be seen by using other methods but DQM solution is smooth and accurate in this case. The results are sensitive to grid distribution in time domain. In light of this, Chebyshev-Gauss-Lobatto distribution performance is excellent. To validate the DQM solutions, the obtained results are compared with those of the characteristic method. In conclusion, DQM is a potential powerful method with minimum computational effort for unsteady flow simulation.

Numerical investigation of temperature distribution on a tunnel boring machine disc cutter affected by geomechanically and excavation parameters

“…Based on the previous DQ studies, uniform or non-uniform grid points can be employed to discretize the temporal and spatial domain. According to the literature and authors’ experiences (Haghighi et al, 2008a, 2008b; Hashemi et al, 2006; Hashemi et al, 2007; Malekzadeh et al, 2006; Malekzadeh and Rahideh, 2007), non-uniform grid points give more accurate results with the same number of grid points. In this research, the spatial domain is divided into non-uniform subintervals based on the Chebyshev–Gauss–Lobatto distribution scheme (Tornabene et al, 2015), as presented in the following. Moreover, the temporal domain is divided based on non-uniform distribution: By employing the DQ rule for both the spatial and the temporal derivatives (Appendix 1), the governing equation can be rewritten as follows: …”

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

“…Differential quadrature method has also been used in different fields of fluid mechanics . In hydraulic and free surface water flow fields, the work completed by Kaya et al to solve a flood propagation problem in open channel, Kaya and Arisoy to solve the Saint‐Venant equations for linear long wave propagation in open channels, Hashemi et al to modeling long waves in shallow water and tidal and surge using incremental DQM, and Hashemi et al to solve the Saint‐Venant equations for numerical simulation of unsteady open channel flow can be pointed out.…”

Verification of Saint-Venant equations solution based on the lax diffusive method for flow routing in natural channels

“…For the same simulation conditions, are shown results generated with the HEC-RAS software (USACE, 2010), a model well established in the literature (PAIVA; COLLISCHONN; BRAVO, 2011;FAN et al, 2012;HAMEED;ALI, 2013). Therefore, the main objective of the study is to evaluate difference of results between distinct procedures for solving the hydrodynamic model, verified for a natural channel that drains an urban area (Iguaçu river), where the flow dynamics is affected by an intense anthropic activity and multiple uses of water.…”

“…In the implicit procedure, the definition of temporal discretization is less restrictive than that of the explicit one, although some studies indicate loss of results quality when increasing the Courant number (GAJDOS; MANDELKERN, 1998;HASHEMI et al, 2007). In this type of method, the solution involves a system of equations, which sometimes causes an increase in the total simulation time due to the size of the matrices (KALITA; SARMA, 2012).…”

“…These expressions constitute a group of hyperbolic and non-linear partial differential equations and, therefore, have no analytical solution except for simplified cases. One of the most applied numerical approximation methods for solving the Saint-Venant equations is the characteristics method (DELPHI, 2011;MENDOZA et al, 2011;LOBEIRO, 2012), whose procedure offers the possibility to define boundary conditions more precisely (HASHEMI et al, 2007).…”