A Parallel High-Order CENO Finite-Volume Scheme with AMR for Three-Dimensional Ideal MHD Flows

2017 ◽  
pp. 343-355 ◽  
Author(s):  
Lucie Freret ◽  
Clinton P. T. Groth ◽  
Hans De Sterck
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
High Order ◽  
Finite Volume Scheme ◽  
Mhd Flows ◽  
Volume Scheme ◽  
Ideal Mhd

A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh

2015 ◽  
Vol 17 (3) ◽  
pp. 615-656 ◽  
Author(s):  
Marc R. J. Charest ◽  
Clinton P. T. Groth ◽  
Pierre Q. Gauthier
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Scheme ◽  
Low Speed ◽  
Volume Scheme

AbstractHigh-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

scholarly journals A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

2015 ◽  
Vol 114 ◽  
pp. 172-192 ◽  
Author(s):  
Marc R.J. Charest ◽  
Thomas R. Canfield ◽  
Nathaniel R. Morgan ◽  
Jacob Waltz ◽  
John G. Wohlbier
Keyword(s):  
Finite Volume ◽  
Compressible Flows ◽  
Three Dimensional ◽  
High Order ◽  
Finite Volume Scheme ◽  
Volume Scheme

scholarly journals High-order central ENO finite-volume scheme for ideal MHD

2013 ◽  
Vol 250 ◽  
pp. 141-164 ◽  
Author(s):  
A. Susanto ◽  
L. Ivan ◽  
H. De Sterck ◽  
C.P.T. Groth
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Ideal Mhd

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.

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