Efficient Riemann Solver Research Articles

Numerical assessment of the potential stream energy extraction of a tidal lagoon inlet

A hypothetical hydrodynamic basin that imitated the Nador lagoon with its inlet was developed to estimate the potential stream energy of the Nador lagoon during a one-month hydrodynamic simulation. The water level rise in the numerical basin was investigated using a depth-averaged hydrodynamic model. The model is based on an unstructured finite volume method to solve the hyperbolic shallow water equations. The method uses an efficient Riemann solver that is balanced with bottom elevation to approximate the convective term. A second Runge-Kutta technique is used to guarantee time marching. Numerical experiments were made to calibrate the model by controlling the bottom frictions in order to simulate the hydrodynamic behaviors. The numerical results of tidal elevation are compared with those from field observations. Good agreements between the numerical model and measurements data were founded. Corresponding current velocity is then used to evaluate potential energy extraction. The results show that the candidate site holds a power density that can achieve 1.246 KW/m2.

Computation of shock waves in plasma

A multitemperature code intended for the numerical solution of the multicomponent gas dynamics equations in problems with a high energy density in matter is described. The velocities of all components with nonzero masses are assumed to be identical. Together with transport of gases with a tabulated equation of state, the code can include electron heat conduction, radiative transfer, energy exchange between the components, and chemical reactions. The gasdynamic part is based on Godunov’s scheme and an efficient Riemann solver with an approximate local equation of state.

A remapping-free, efficient Riemann-solvers based, ALE method for multi-material fluids with general EOS

Based on an efficient Riemann solver, a remapping-free ALE method (RALE) for multi-material fluids with general equations of state is proposed. The basic idea of constructing the RALE is to couple the Lagrangian method with a remapping-free ALE-type method. In order to keep the sharpness of a material interface, the Lagrangian formulation is employed for tracking the material interface, where the Lagrangian velocity of nodes and Lagrangian fluxes are designed. In single material regions, the numerical fluxes are constructed on moving meshes which move nodes to the regions with large gradients to increase the numerical accuracy, and the explicit remapping stage is avoided because of the new discrete scheme. The inverse Hermite interpolation argument is employed in solving the Riemann problem with general EOS, consequently, reducing iteration steps greatly and resulting in an efficient and robust Riemann solver. A number of numerical examples are presented.

An accurate and efficient Riemann solver with tangent velocities for Godunov schemes in special relativistic hydrodynamics

AbstractIn order to numerically integrate the special relativistic hydrodynamics (SRHD) equations through a Godunov scheme, the use of an exact Riemann solver having a low computational cost is proposed. The solver works through a Newton iterative method in pressure, by using a preliminary detection of the wave pattern and an integration by series of the ODE for the normal velocity across a rarefaction wave. A comparison with the solver of Martì and Müller shows about a 90% reduction of the computational cost. The present Riemann solver has been used inside a first‐order Godunov scheme, in order to test the solver for high jumps of the primitive variables, perhaps avoiding certain numerical manipulations (e.g. limiting filters and multi‐step integration schemes). The time evolution of a two‐dimensional mixing layer is finally considered and a comparison with the solution obtained from a HLL method is carried out.The main result of this analysis lies in showing how the present exact Riemann solver can be successfully employed in the effective numerical integration of the SRHD equations. Copyright © 2009 John Wiley & Sons, Ltd.

An efficient Riemann solver for open channel flows

An efficient numerical method is developed for the one-dimensional open channel flow equations. The scheme is a modification of one presented recently, but with an improvement in the efficiency made through the use of the arithmetic mean as an average of flow variables across the interface between adjacent states. Numerical results are shown for two problems, and an indication of the efficiency gained is given.

An efficient Riemann solver for unsteady flows with non-ideal gases

A Riemann solver is presented for the Euler equations of gas dynamics with real gases. This represents a more efficient version of an algorithm originally presented by the author.