Hybrid Artificial Viscosity–Central-Upwind Scheme for Recirculating Turbulent Shallow Water Flows

2019 ◽  
Vol 145 (12) ◽  
pp. 04019041 ◽  
Author(s):  
Bobby Minola Ginting ◽  
Herli Ginting
Keyword(s):  
Shallow Water ◽  
Artificial Viscosity ◽  
Upwind Scheme ◽  
Water Flows ◽  
Shallow Water Flows

scholarly journals Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows

2016 ◽  
Vol 136 ◽  
pp. 193-206 ◽  
Author(s):  
Abdelaziz Beljadid ◽  
Abdolmajid Mohammadian ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Upwind Scheme ◽  
Positivity Preserving ◽  
Water Flows ◽  
Shallow Water Flows

scholarly journals A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels

2021 ◽  
Author(s):  
Gerardo Hernandez-Duenas ◽  
Jorge Balbás
Keyword(s):  
Shallow Water ◽  
Cross Sections ◽  
Bottom Topography ◽  
Coefficient Matrix ◽  
Upwind Scheme ◽  
One Dimensional ◽  
Hyperbolic Conservation ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Entropy Inequalities

We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These flows are described by a conditionally hyperbolic balance law  with non-conservative products. A detailed description of the properties of the model is provided, including entropy inequalities and asymptotic approximations of the eigenvalues of the corresponding coefficient matrix. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic conservation and balance laws and it satisfies two properties crucial for the accurate simulation of shallow-water flows: it {\it preserves the positivity} of the water depth for each layer, and it is {\it well balanced}, {\it i.e.}, the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. Along with the description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.

Assessing the Numerical Accuracy of Complex Spherical Shallow-Water Flows

2007 ◽  
Vol 135 (11) ◽  
pp. 3876-3894 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
David G. Dritschel
Keyword(s):  
Shallow Water ◽  
Fourth Order ◽  
Large Scale ◽  
Numerical Accuracy ◽  
Conservation Of Energy ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Low Froude Number ◽  
Contour Advection ◽  
High Reynolds

Abstract The representation of nonlinear shallow-water flows poses severe challenges for numerical modeling. The use of contour advection with contour surgery for potential vorticity (PV) within the contour-advective semi-Lagrangian (CASL) algorithm makes it possible to handle near-discontinuous distributions of PV with an accuracy beyond what is accessible to conventional algorithms used in numerical weather and climate prediction. The emergence of complex distributions of the materially conserved quantity PV, in the absence of forcing and dissipation, results from large-scale shearing and deformation and is a common feature of high Reynolds number flows in the atmosphere and oceans away from boundary layers. The near-discontinuous PV in CASL sets a limit on the actual numerical accuracy of the Eulerian, grid-based part of CASL. For the spherical shallow-water equations, the limit is studied by comparing the accuracy of CASL algorithms with second-order-centered, fourth-order-compact, and sixth-order-supercompact finite differencing in latitude in conjunction with a spectral treatment in longitude. The comparison is carried out on an unstable midlatitude jet at order one Rossby number and low Froude number that evolves into complex vortical structures with sharp gradients of PV. Quantitative measures of global conservation of energy and angular momentum, and of imbalance as diagnosed using PV inversion by means of Bolin–Charney balance, indicate that fourth-order differencing attains the highest numerical accuracy achievable for such nonlinear, advectively dominated flows.

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