A projection method for shallow water equations

Adaptivity in space and time for shallow water equations

“…Figure 4 shows the mean critical time step (as calculated in Section 2) for all mesh nodes in three situations; note that mesh adaptation allows higher stability limits than the initial mesh. This can also be seen in the equations of the stability analysis: the critical time step results to be inversely proportional to D=U/(k 1 2 H), where k 1 is Chezy's constant, g is the gravity, U is the modulus of the computed velocity (i.e. comprises the approximation errors in time and in space) and H is the depth.…”

“…In a previous paper [1], an algorithm for solving the shallow water equations was presented. Here we will sketch it briefly and make some considerations.…”

“…6.2. Computation of (ZU**) (n + 1) Domain decomposition for Equation (2.4) was still considered in [1]. It is based on non-overlapping subdomains defined by choosing regions (not necessarily contiguous) of the lagoon at constant depth.…”

“…A numerical method for solving the shallow water equations applied to the Venice Lagoon was developed earlier [1][2][3]. Here, adaptivity [4,5] for space and time discretizations and algorithm decoupling in time are introduced.…”

Simulação numérica 3D do enchimento de compartimentos de reservatórios utilizando o método de elementos finitos

“…Modelos 2D, que não calculam rigorosamente o perfil hidrodinâmico, entre outros efeitos, na orientação da profundidade,é chamado de modelo deáguas rasas, e nele as equações de Navier-Stokes sofrem uma grande simplificação. O trabalho de Cecchi [Cecchi et al, 1998] apresenta o esforço de simulação do comportamento da lagoa de Veneza com as equações de Navier-Stokes simplificadas para a aproximação deáguas rasas e com uma malha computacional ajustada para o método dos elementos finitos.…”