scholarly journals CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes

2021 ◽  
Vol 89 (3) ◽  
Author(s):  
Panagiotis Tsoutsanis ◽  
Ebenezer Mayowa Adebayo ◽  
Adrian Carriba Merino ◽  
Agustin Perez Arjona ◽  
Martin Skote
Keyword(s):  
Finite Volume ◽  
Analytical Solutions ◽  
Unstructured Meshes ◽  
Accurate Solution ◽  
High Order ◽  
Experimental Results ◽  
Test Problems ◽  
Interface Capturing ◽  
Multicomponent Flows ◽  
Stringent Test

AbstractIn this paper we extend the application of unstructured high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to multicomponent flows using the interface capturing paradigm. The developed method achieves high-order accurate solution in smooth regions, while providing oscillation free solutions at discontinuous regions. The schemes are inherently compact in the sense that the central stencils employed are as compact as possible, and that the directional stencils are reduced in size, therefore simplifying their implementation. Several parameters that influence the performance of the schemes are investigated, such as reconstruction variables and their reconstruction order. The performance of the schemes is assessed under a series of stringent test problems consisting of various combinations of gases and liquids, and compared against analytical solutions, computational and experimental results available in the literature. The results obtained demonstrate the robustness of the new schemes for several applications, as well as their limitations within the present interface-capturing implementation.

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.

The Simulation of the Linearized Euler Equations by a Second Order Scheme is Possible

2005 ◽  
Vol 4 (1-2) ◽  
pp. 49-68
Author(s):  
R. Abgrall ◽  
M. Ravachol ◽  
S. Marret
Keyword(s):  
Numerical Simulation ◽  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Complex Geometries ◽  
Residual Distribution ◽  
Linearized Euler Equations ◽  
Order Scheme ◽  
The One

We are interested in the numerical simulation of acoustic perturbations via the linearized Euler equations using triangle unstructured meshes in complex geometries such as the one around a complete aircraft. It is known that the classical schemes using a finite volume formulation with high order extrapolation of the variables can be very disappointing. In this paper, we show that using an upwind residual distribution formulation, it is possible to simulate such problems, even on truly unstructured meshes. The main focus of the paper is on the propagative properties of the scheme.

scholarly journals A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws

2014 ◽  
Vol 16 (3) ◽  
pp. 718-763 ◽  
Author(s):  
Raphaël Loubère ◽  
Michael Dumbser ◽  
Steven Diot
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Conservation Laws ◽  
Unstructured Meshes ◽  
High Order ◽  
Mhd Equations ◽  
Optimal Order ◽  
Finite Volume Scheme ◽  
Hyperbolic Conservation ◽  
2D And 3D

AbstractIn this paper, we investigate the coupling of the Multi-dimensional Optimal Order Detection (MOOD) method and the Arbitrary high order DERivatives (ADER) approach in order to design a new high order accurate, robust and computationally efficient Finite Volume (FV) scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions, respectively. The Multi-dimensional Optimal Order Detection (MOOD) method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes. It is an arbitrary high-order accurate Finite Volume scheme in space, using polynomial reconstructions witha posterioridetection and polynomial degree decrementing processes to deal with shock waves and other discontinuities. In the following work, the time discretization is performed with an elegant and efficient one-step ADER procedure. Doing so, we retain the good properties of the MOOD scheme, that is to say the optimal high-order of accuracy is reached on smooth solutions, while spurious oscillations near singularities are prevented. The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D, but it also increases the stability of the overall scheme. A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost, robustness, accuracy and efficiency. The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive (memory and/or CPU time), or because it is more accurate for a given grid resolution. A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws: the Euler equations of compressible gas dynamics, the classical equations of ideal magneto-Hydrodynamics (MHD) and finally the relativistic MHD equations (RMHD), which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation. All tests are run on genuinely unstructured grids composed of simplex elements.

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