Application of Dual-Time Stepping and Finite-Volume Scheme in Computational Aeroacoustics

2006 ◽  
Author(s):  
Wen Lin ◽  
Pratt & Whitney Rocketdyne
Keyword(s):  
Finite Volume ◽  
Computational Aeroacoustics ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Time Stepping ◽  
Dual Time Stepping

A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

2011 ◽  
Vol 9 (1) ◽  
pp. 205-230 ◽  
Author(s):  
Angela Ferrari ◽  
Claus-Dieter Munz ◽  
Bernhard Weigand
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Indicator Function ◽  
Finite Volume Scheme ◽  
Riemann Solver ◽  
Time Step ◽  
Material Interface ◽  
Volume Scheme ◽  
Time Stepping ◽  
Local Time Stepping

AbstractIn this paper, a new sharp-interface approach to simulate compressible multiphase flows is proposed. The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order path-conservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface. At the interface our method applies ghost cells to compute the numerical flux, as the ghost fluid method. However, unlike the original ghost fluid scheme of Fedkiw et al. [15], the state of the ghost fluid is derived from an approximate-state Riemann solver, similar to the approach proposed in [25], but based on a much simpler formulation. Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface, instead of the system used in [25]. Away from the interface, we use the new general Osher-type flux recently proposed by Dumbser and Toro [13], which is a simple but complete Riemann solver, applicable to general hyperbolic conservation laws. The time integration is performed using a fully-discrete one-step scheme, based on the approaches recently proposed in [5,7]. This allows us to evolve the system also with time-accurate local time stepping. Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme, a local evolution for the indicator function is applied, which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step. The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme. Two different fluids have been used, namely an ideal gas and a weakly compressible fluid modeled by the Tait equation. Several tests have been computed to assess the accuracy and the performance of the new high order scheme. A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions. The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.

A conservative finite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids

2015 ◽  
Vol 86 ◽  
pp. 217-230 ◽  
Author(s):  
José Rafael Cavalcanti ◽  
Michael Dumbser ◽  
David da Motta-Marques ◽  
Carlos Ruberto Fragoso Junior
Keyword(s):  
Local Time ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Scalar Transport ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Time Stepping ◽  
Local Time Stepping

scholarly journals Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme

2010 ◽  
Vol 234 (7) ◽  
pp. 2089-2097 ◽  
Author(s):  
X. Nogueira ◽  
I. Colominas ◽  
L. Cueto-Felgueroso ◽  
S. Khelladi ◽  
F. Navarrina ◽  
...  
Keyword(s):  
Finite Volume ◽  
Unstructured Grids ◽  
Higher Order ◽  
Computational Aeroacoustics ◽  
Finite Volume Scheme ◽  
Volume Scheme

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals A 3D finite volume scheme for the simulation of edge plasma in Tokamaks

2013 ◽  
Vol 43 ◽  
pp. 164-179
Author(s):  
M. Bilanceri ◽  
L. Combe ◽  
H. Guillard ◽  
B. Nkonga ◽  
A. Sangam
Keyword(s):  
Finite Volume ◽  
Edge Plasma ◽  
Finite Volume Scheme ◽  
Volume Scheme
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