Upwind Scheme

This article is devoted to the study of a hybrid numerical scheme for a class of singularly perturbed parabolic convection-diffusion problems with discontinuous convection coefficients. In general, the solutions of this class of problems possess strong interior ...

This paper presents a new finite volume discretization methodology for the solution of transport equations on locally refined or unstructured Cartesian meshes. The implementation of the cell-face values of the dependent variables enables the employment of data from remote cells and thus the use of higher-order differencing schemes. It also results in simple and flux-conservative multiple-scale stencils for the discretization of the governing equations. The latter are finally cast into a generalized form that does not depend on the local mesh structure. The performance of the numerical model is demonstrated on some classical 2D problems using various gridding techniques and a bounded second-order upwind scheme. A stable and efficient behaviour of the algorithm is observed in all test cases. The results indicate that the combination in the present model of both local grid refinement and second-order discretization can produce substantially more accurate solutions than each of the above techniques alone, for the same computational effort. The method is also applicable to turbulent flows and can be easily extended to three-dimensions.

... Miles Zengeya a , Mohamed Gadala a * & Guus Segal b pages 947-968. ... 159 – 170 , 1962 . [CrossRef] View all references] and Ezzat and Rohde [88. HA Ezzat and SM Rohde , A Study of the Thermohydrodynamic Performance of Finite Slider Bearings , Trans. ASME, J. Lub. ...

A generalisation of the theta time discretisation scheme is proposed for advection problems with strongly varying meshes and velocity profiles. Starting point is the theta upwind scheme, which is conservative, stable, positivity-preserving, and free of spurious oscillations for any given time step, provided that theta is sufficiently large. The main disadvantage of this scheme is the accompanying numerical diffusion,

A simple unstructured finite volume scheme is used to solve the two-dimensional
shallow water equations (SWEs) for simulation of dam break flows over irregular beds
involving wet and dry interfaces. In space, we construct a balancing higher order upwind
scheme on unstructured triangular mesh to approximate the convective and source term
due to bed slop. We improve the scheme to treat the cases of flow over dry beds. For
temporal derivative approximation, a second-order explicit Runge-Kutta is used. We
apply the scheme for several theoretical two-dimensional numerical experiments
involving dam-break flows with moving wet-dry fronts over irregular bed topography.
Promising results are obtained.

A simple unstructured finite volume scheme is used to solve the two-dimensional
shallow water equations (SWEs) for simulation of dam break flows over irregular beds
involving wet and dry interfaces. In space, we construct a balancing higher order upwind
scheme on unstructured triangular mesh to approximate the convective and source term
due to bed slop. We improve the scheme to treat the cases of flow over dry beds. For
temporal derivative approximation, a second-order explicit Runge-Kutta is used. We
apply the scheme for several theoretical two-dimensional numerical experiments
involving dam-break flows with moving wet-dry fronts over irregular bed topography.
Promising results are obtained

In this work we present an upwind-based high resolution scheme using flux limiters. Based on the direction of flow we choose the smoothness parameter in such a way that it leads to a truly upwind scheme without losing total variation diminishing (TVD) property for hyperbolic ...

In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tome and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulen...

We propose a new third-order multidimensional upwind algorithm for the solution of the flow equations on tetrahedral cells unstructured grids. This algorithm has a compact stencil (cell-based computations) and uses a finite element idea when computing the residual over the cell to achieve its third-order (spatial) accuracy. The construction of the new scheme is presented. The asymptotic accuracy for steady or unsteady, inviscid or viscous flow situations is proved using numerical experiments. The new high-order discretization proves to have excellent parallel scalability. Our studies show the advantages of the new compact third-order scheme when compared with the classical second-order multidimensional upwind schemes.

ABSTRACT A multidimensional discretisation of the shallow water equations governing unsteady free-surface flow is proposed. The method, based on a residual distribution discretisation, relies on a characteristic eigenvector decomposition of each cell residual, and the use of appropriate distribution schemes. For uncoupled equations, multidimensional convection schemes on compact stencils are used, while for coupled equations, either system distribution schemes such as the Lax-Wendroff scheme or scalar schemes may be used. For steady subcritical flows, the equations can be partially diagonalised into a purely convective equation of hyperbolic nature, and a set of coupled equations of elliptic nature. The multidimensional discretisation, which is second-order-accurate at steady state, is shown to be superior to the standard Lax-Wendroff discretisation. For steady supercritical flows, the equations can be fully diagonalised into a set of convective equations corresponding to the steady state characteristics. Discontinuities such as hydraulic jumps, are captured in a sharp and non-oscillatory way. For unsteady flows, the characteristic equations remain coupled. An appropriate treatment of the coupling terms allows the discretisation of these equations at the scalar level. Although presently only first-order-accurate in space and time, the classical dam-break problem demonstrates the validity of the approach.