scholarly journals Discrete Boltzmann model of shallow water equations with polynomial equilibria

2018 ◽  
Vol 29 (09) ◽  
pp. 1850080 ◽  
Author(s):  
Jianping Meng ◽  
Xiao-Jun Gu ◽  
David R. Emerson ◽  
Yong Peng ◽  
Jianmin Zhang
Keyword(s):  
Shallow Water ◽  
Hermite Expansion ◽  
Water Flows ◽  
Order Expansion ◽  
Shallow Water Flows ◽  
Steady Solutions ◽  
Supercritical Flows ◽  
Boltzmann Model ◽  
The Impact ◽  
Higher Order Expansion

A type of discrete Boltzmann model for simulating shallow water flows is derived by using the Hermite expansion approach. Through analytical analysis, we study the impact of truncating distribution function and discretizing particle velocity space. It is found that the convergence behavior of expansion is nontrivial while the conservation laws are naturally satisfied. Moreover, the balance of source terms and flux terms for steady solutions is not sacrificed. Further numerical validations show that the capability of simulating supercritical flows is enhanced by employing higher-order expansion and quadrature.

A multispeed Discrete Boltzmann Model for transcritical 2D shallow water flows

2015 ◽  
Vol 284 ◽  
pp. 117-132 ◽  
Author(s):  
Michele La Rocca ◽  
Andrea Montessori ◽  
Pietro Prestininzi ◽  
Sauro Succi
Keyword(s):  
Shallow Water ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Boltzmann Model

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.

Sign in / Sign up

Export Citation Format

Share Document