The Strait of Gibraltar-A Border between Worlds (English title) In The Strait of Gibraltar,centuries overlap,events collide and history repeats itself.This improbable border between-a Europe and Mrica is one of the mo...The Strait of Gibraltar-A Border between Worlds (English title) In The Strait of Gibraltar,centuries overlap,events collide and history repeats itself.This improbable border between-a Europe and Mrica is one of the most significant regions in the world,not the least because of the numerous myths and legends that people associate with the region. Mythologies are still alive here,in this immemorial refuge that nothing reaches, as if it were impervious to time.展开更多
A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography.The governing equations are refo...A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography.The governing equations are reformulated as a non-linear system of conservation laws with differential source forces and reaction terms.Coupling between theflow layers is accounted for in the system using a set of ex-change relations.The considered well-balanced Runge-Kutta discontinuous Galerkin method is a locally conservativefinite element method whose approximate solutions are discontinuous across the inter-element boundaries.The well-balanced property is achieved using a special discretization of source terms that depends on the nature of hydrostatic solutions along with the Gauss-Lobatto-Legendre nodes for the quadra-ture used in the approximation of source terms.The method can also be viewed as a high-order version of upwindfinite volume solvers and it offers attractive features for the numerical solution of conservation laws for which standardfinite element methods fail.To deal with the source terms we also implement a high-order splitting operator for the time integration.The accuracy of the proposed Runge-Kutta discontinuous Galerkin method is examined for several examples of multilayer free-surfaceflows over bothflat and non-flat beds.The performance of the method is also demonstrated by comparing the results obtained using the proposed method to those obtained using the incompressible hydrostatic Navier-Stokes equations and a well-established kinetic method.The proposed method is also applied to solve a recirculationflow problem in the Strait of Gibraltar.展开更多
We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of...We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation.The dispersion of free-surface temperature is modelled by an advection-diffusion equation.Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure.Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations.In addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms.We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.展开更多
文摘The Strait of Gibraltar-A Border between Worlds (English title) In The Strait of Gibraltar,centuries overlap,events collide and history repeats itself.This improbable border between-a Europe and Mrica is one of the most significant regions in the world,not the least because of the numerous myths and legends that people associate with the region. Mythologies are still alive here,in this immemorial refuge that nothing reaches, as if it were impervious to time.
文摘A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography.The governing equations are reformulated as a non-linear system of conservation laws with differential source forces and reaction terms.Coupling between theflow layers is accounted for in the system using a set of ex-change relations.The considered well-balanced Runge-Kutta discontinuous Galerkin method is a locally conservativefinite element method whose approximate solutions are discontinuous across the inter-element boundaries.The well-balanced property is achieved using a special discretization of source terms that depends on the nature of hydrostatic solutions along with the Gauss-Lobatto-Legendre nodes for the quadra-ture used in the approximation of source terms.The method can also be viewed as a high-order version of upwindfinite volume solvers and it offers attractive features for the numerical solution of conservation laws for which standardfinite element methods fail.To deal with the source terms we also implement a high-order splitting operator for the time integration.The accuracy of the proposed Runge-Kutta discontinuous Galerkin method is examined for several examples of multilayer free-surfaceflows over bothflat and non-flat beds.The performance of the method is also demonstrated by comparing the results obtained using the proposed method to those obtained using the incompressible hydrostatic Navier-Stokes equations and a well-established kinetic method.The proposed method is also applied to solve a recirculationflow problem in the Strait of Gibraltar.
基金support by the DeutscheForschungsGemeinschaft(DFG)under grant No.KL 1105/9.
文摘We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation.The dispersion of free-surface temperature is modelled by an advection-diffusion equation.Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure.Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations.In addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms.We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.
