A physically based flux limiter for QUICK calculations of advective scalar transport

Abstract

SUMMARYTransient, advective transport of a contaminant into a clean domain will exhibit a moving sharp front that separates contaminated and clean regions. Due to 'numerical diffusion'-the combined effects of 'crosswind diffusion' and 'artificial dispersion'-a numerical solution based on a first-order (upwind) treatment will smear out the sharp front. The use of higher-order schemes, e.g. QUICK (quadratic upwinding) reduces the smearing but can introduce non-physical oscillations in the solution. A common approach to reduce numerical diffusion without oscillations is to use a scheme that blends low-order and high-order approximations of the advective transport. Typically, the blending is based on a parameter that measures the local monotonicity in the predicted scalar field. In this paper, an alternative approach is proposed for use in scalar transport problems where physical bounds C Low C C High on the scalar are known a priori. For this class of problems, the proposed scheme switches from a QUICK approximation to an upwind approximation whenever the predicted upwind nodal value falls outside of the physical range [C Low , C High ]. On two-dimensional steady-state and one-dimensional transient test problems predictions obtained with the proposed scheme are essentially indistinguishable from those obtained with monotonic flux-limiter schemes. An analysis of the modified equation explains the observed performance of first-and second-order time-stepping schemes in predicting the advective transport of a step. In application to the transient two-dimensional problem of contaminate transport into a streambed, predictions obtained with the proposed flux-limiter scheme agree with those obtained with a scheme from the literature.

Experimental Study of the Solute Transport in the Interfacial Exchange Zone (IEZ) of a Gravel Stream Bed

“…Coupled 2-D hydrodynamic and solute transport models were previously developed in Qian et al (2007aQian et al ( , 2007bQian et al ( , 2008Qian et al ( , 2009) to better estimate vertical enhanced dispersion coefficients (D E ) for solutes in a porous and permeable stream bed. Turbulence parameterized by bed shear stress, surface wave parameterized by longitudinal dispersivity to wave length ratio and wave steepness, as well as sediment hydraulic conductivity and sediment porosity were included in the model as independent variables.…”

“…A coupled two-dimensional hydrodynamic and solute transport model for the experiment setup was developed from the basic governing equations by Qian et al, (2007aQian et al, ( , 2007bQian et al, ( , 2008Qian et al, ( , and 2009). The pressure head distribution, h(x, 0), is induced by the interaction and cumulative effect of turbulence (pressure pulse model, Higashino et al, 2009) in the overlying stream flow, of underflow through the streambed, and of the surface wave induced advective exchange flow from the overlying water through the pores of a sediment bed.…”

A Simple 2nd-order Physically Bounded Convective Scheme

“…It should be stressed that the measures used in HR schemes always involve information of three consecutive cells, including a far-upwind cell. Qin Qian, et al, constructed a new scheme which is a combination of QUICK and FUD scheme, using the upwind nodal value as the measure [1].…”

“…In tradition, the high-resolutions (HR) schemes that use some parameters to measure the local monotonicity in the predicted scalar field, including the well-known TVD-type and NVD-type schemes, are widely used. Recently, Qin Qian, et al, [1] proposed a new approach which use the upwind approximation as the 'unbounded indicator". During the computation, the actual scheme switches between QUICK scheme and 1st-order upwind (FUD) scheme, according to whether the indicator locates in the range of physical bounds or not.…”

Modeling of Solute Transport in Pore Scale Sediment Beds: A Summary of Hydrodynamic Interactions Induced by Surface Wave, Bed Form, and Near Bed Turbulence

“…A third-order Quadratic Upstream Interpolation for Convective Kinematics (QUICK) (Leonard 1977) scheme written in terms of nodal-point values of the advected variable has been applied (Qian, et al 2007a) to decrease the numerical dissipation (smear). The physically based (phib) flux-limiter (Qian, et al 2007b) is adopted to diminish the numerical dispersion.…”