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H Van Der Ven - One of the best experts on this subject based on the ideXlab platform.

  • space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation
    Journal of Computational Physics, 2002
    Co-Authors: J J W Van Der Vegt, H Van Der Ven
    Abstract:

    A new space-time discontinuous Galerkin finite element method for the solution of the Euler Equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient elementwise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated. The non-Linear Equations of the space-time discretization are solved using a multigrid accelerated pseudo-time-integration technique with an optimized Runge-Kutta method. The Linear stability of the pseudo-time-integration method is investigated for the Linear Advection Equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that using the data at the superconvergence points, the accuracy of the numerical discretization is O(h5/2) in space for smooth subsonic flows, both on structured and on locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.

J J W Van Der Vegt - One of the best experts on this subject based on the ideXlab platform.

  • space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation
    Journal of Computational Physics, 2002
    Co-Authors: J J W Van Der Vegt, H Van Der Ven
    Abstract:

    A new space-time discontinuous Galerkin finite element method for the solution of the Euler Equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient elementwise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated. The non-Linear Equations of the space-time discretization are solved using a multigrid accelerated pseudo-time-integration technique with an optimized Runge-Kutta method. The Linear stability of the pseudo-time-integration method is investigated for the Linear Advection Equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that using the data at the superconvergence points, the accuracy of the numerical discretization is O(h5/2) in space for smooth subsonic flows, both on structured and on locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.

Vincent Guinot - One of the best experts on this subject based on the ideXlab platform.

  • a finite volume upwind scheme for the solution of the Linear Advection diffusion Equation with sharp gradients in multiple dimensions
    Advances in Water Resources, 2007
    Co-Authors: Fabiola Badrotnico, Francois Brissaud, Vincent Guinot
    Abstract:

    Abstract A finite volume upwind numerical scheme for the solution of the Linear Advection Equation in multiple dimensions on Cartesian grids is presented. The small-stencil, Modified Discontinuous Profile Method (MDPM) uses a sub-cell piecewise constant reconstruction and additional information at the cell interfaces, rather than a spatial extension of the stencil as in usual methods. This paper presents the MDPM profile reconstruction method in one dimension and its generalization and algorithm to two- and three-dimensional problems. The method is extended to the Advection–diffusion Equation in multiple dimensions. The MDPM is tested against the MUSCL scheme on two- and three-dimensional test cases. It is shown to give high-quality results for sharp gradients problems, although some scattering appears. For smooth gradients, extreme values are best preserved with the MDPM than with the MUSCL scheme, while the MDPM does not maintain the smoothness of the original shape as well as the MUSCL scheme. However the MDPM is proved to be more efficient on coarse grids in terms of error and CPU time, while on fine grids the MUSCL scheme provides a better accuracy at a lower CPU.

Sergio Pirozzoli - One of the best experts on this subject based on the ideXlab platform.

  • a general strategy for the optimization of runge kutta schemes for wave propagation phenomena
    Journal of Computational Physics, 2009
    Co-Authors: Matteo Bernardini, Sergio Pirozzoli
    Abstract:

    We analyze optimized explicit Runge-Kutta schemes (RK) for computational aeroacoustics, and wave propagation phenomena in general. Exploiting the analysis developed in [S. Pirozzoli, Performance analysis and optimization of finite-difference schemes for wave propagation problems, J. Comput. Phys. 222 (2007) 809-831], we rigorously evaluate the performance of several time integration schemes in terms of appropriate error and cost metrics, and provide a general strategy to design Runge-Kutta methods tailored for specific applications. We present families of optimized second- and third-order Runge-Kutta schemes with up to seven stages, and describe their implementation in the framework of Williamson's 2N-storage formulation [J.H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35 (1980) 48-56]. Numerical simulations of the 1D Linear Advection Equation and of the 2D Linearized Euler Equations are performed to demonstrate the validity of the theory and to quantify the improvement provided by optimized schemes.

Mikhail Pavlovich Galanin - One of the best experts on this subject based on the ideXlab platform.

  • nonLinear monotonization of the babenko scheme for the quasi Linear Advection Equation 1
    Mathematical Modelling and Analysis, 2005
    Co-Authors: T A Alexandrikova, Mikhail Pavlovich Galanin
    Abstract:

    Abstract The paper is devoted to construction and development of new method for numerical solution of hyperbolic type Equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different finite‐difference schemes on 4 point patterns for the simplest hyperbolic Equation: Linear Advection Equation. This Equation has the main features of every hyperbolic Equation and is the important part of many mathematical models. In other cases the Advection operator is the important part of the full operator of the problem. All 26 schemes have been compared experimentally on the special representative set of tests. Nevertheless to simplicity of the Equation, almost all schemes have different disadvantages. They are discussed in detail in the cited papers. So, the investigation of new schemes for this Equation is still an important task. In [4, 5, 6, 7, 8, 9] some new schemes were constructed for solving this Advection Equation. The nonLinear monoton...