Abstract
In this paper we present the Large Time Step method based
on the Roe scheme applied to a standard two-fluid model.
The Large Time Step method was originally developed in
the nineteen eighties by Randall LeVeque and has enjoyed
increasing popularity in the CFD community in recent years
due to its attractive features such as increased accuracy and
efficiency compared to its standard low time step counterparts.
In terms of efficiency and computation time, one of
the main disadvantages in common explicit schemes is the
limited time step size imposed by the CFL condition. The
idea behind the Large Time Step method is to increase the
domain of dependence which leads to a relaxation of the
CFL condition, allowing us to use Courant numbers larger
than one, i.e. using very large time steps compared to standard
explicit methods. It is shown that such an approach
notably reduces the computation time and increases the accuracy
of the solution. However, the idea of increasing the
domain of dependence causes difficulties when it comes to
boundary treatment, especially in the presence of source
terms. In this paper, we describe and address these diffi-
culties. We extend the standard Roe scheme with the Large
Time Step method and apply it to the standard two-fluid
model for the water faucet test case, focusing on the treatment of the boundary conditions. Furthermore, we compare the performance of the scheme with the classical Roe scheme in terms of computational time.
on the Roe scheme applied to a standard two-fluid model.
The Large Time Step method was originally developed in
the nineteen eighties by Randall LeVeque and has enjoyed
increasing popularity in the CFD community in recent years
due to its attractive features such as increased accuracy and
efficiency compared to its standard low time step counterparts.
In terms of efficiency and computation time, one of
the main disadvantages in common explicit schemes is the
limited time step size imposed by the CFL condition. The
idea behind the Large Time Step method is to increase the
domain of dependence which leads to a relaxation of the
CFL condition, allowing us to use Courant numbers larger
than one, i.e. using very large time steps compared to standard
explicit methods. It is shown that such an approach
notably reduces the computation time and increases the accuracy
of the solution. However, the idea of increasing the
domain of dependence causes difficulties when it comes to
boundary treatment, especially in the presence of source
terms. In this paper, we describe and address these diffi-
culties. We extend the standard Roe scheme with the Large
Time Step method and apply it to the standard two-fluid
model for the water faucet test case, focusing on the treatment of the boundary conditions. Furthermore, we compare the performance of the scheme with the classical Roe scheme in terms of computational time.