The Space-Time CE/SE Method for Solving Reduced Two-Fluid Flow Model

2012 ◽  
Vol 12 (4) ◽  
pp. 1070-1095 ◽  
Author(s):  
Shamsul Qamar ◽  
Munshoor Ahmed ◽  
Ishtiaq Ali
Keyword(s):  
Finite Volume ◽  
Numerical Test ◽  
Current Method ◽  
Space Time ◽  
Finite Volume Schemes ◽  
Reconstruction Procedure ◽  
Flow Equations ◽  
Flow Models ◽  
Two Fluids ◽  
Two Fluid

AbstractThe space-time conservation element and solution element (CE/SE) method is proposed for solving a conservative interface-capturing reduced model of compressible two-fluid flows. The flow equations are the bulk equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term for accounting the energy exchange. The one and two-dimensional flow models are numerically investigated in this manuscript. The CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building block of the suggested method. The method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation. In order to reveal the efficiency and performance of the approach, several numerical test cases are presented. For validation, the results of the current method are compared with other finite volume schemes.

scholarly journals Large-time behaviour of a family of finite volume schemes for boundary-driven convection–diffusion equations

2019 ◽  
Vol 40 (4) ◽  
pp. 2473-2504 ◽  
Author(s):  
Claire Chainais-Hillairet ◽  
Maxime Herda
Keyword(s):  
Finite Volume ◽  
Exponential Decay ◽  
Large Time ◽  
Nonlinear Models ◽  
Numerical Test ◽  
Diffusion Equations ◽  
Time Behaviour ◽  
Finite Volume Schemes ◽  
Large Time Behaviour ◽  
Convection Diffusion

Abstract We are interested in the large-time behaviour of solutions to finite volume discretizations of convection–diffusion equations or systems endowed with nonhomogeneous Dirichlet- and Neumann-type boundary conditions. Our results concern various linear and nonlinear models such as Fokker–Planck equations, porous media equations or drift–diffusion systems for semiconductors. For all of these models, some relative entropy principle is satisfied and implies exponential decay to the stationary state. In this paper we show that in the framework of finite volume schemes on orthogonal meshes, a large class of two-point monotone fluxes preserves this exponential decay of the discrete solution to the discrete steady state of the scheme. This includes for instance upwind and centred convections or Scharfetter–Gummel discretizations. We illustrate our theoretical results on several numerical test cases.

scholarly journals ADER-WENO finite volume schemes with space–time adaptive mesh refinement

2013 ◽  
Vol 248 ◽  
pp. 257-286 ◽  
Author(s):  
Michael Dumbser ◽  
Olindo Zanotti ◽  
Arturo Hidalgo ◽  
Dinshaw S. Balsara
Keyword(s):  
Finite Volume ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Space Time ◽  
Finite Volume Schemes

scholarly journals Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

2013 ◽  
Vol 14 (5) ◽  
pp. 1174-1206 ◽  
Author(s):  
Walter Boscheri ◽  
Michael Dumbser
Keyword(s):  
Finite Volume ◽  
Space Time ◽  
High Order ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Triangular Meshes ◽  
Finite Volume Schemes ◽  
Local Space ◽  
One Step ◽  
Time Basis

AbstractIn this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in. For that purpose, a new element-local weak formulation of the governing PDE is adopted on moving space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes withstraightedges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.

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