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This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
This paper is concerned with the numerical approximations of Cauchy problems for
one-dimensional nonconservative hyperbolic systems.
The first goal is to introduce a general concept of well-balancing
for numerical schemes solving this kind of systems. Once this concept stated, we
investigate the well-balance properties of numerical schemes based on the
generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory
is applied to obtain well-balanced...
Surface waves of finite amplitude originated by the vertical oscillations of a container are studied. The existence of both supercritical and subcritical waves is found which are either synchronous or subharmonic with respect to the basic oscillation.
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
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