Chuenjarern, Nattaporn

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Chuenjarern, Nattaporn
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nattaporn.ch@kmitl.ac.th

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    Item type:Publication,
    Maximum-principle-preserving high-order discontinuous Galerkin methods for incompressible Euler equations on overlapping meshes
    (2024-01-15)
    Tian, Lulu
    ;
    Chuenjarern, Nattaporn
    ;
    Guo, Hui
    ;
    Yang, Yang
    In this paper, we construct a new local discontinuous Galerkin (LDG) algorithm to solve the incompressible Euler equation in two space dimensions on overlapping meshes. This method solves the vorticity, velocity field and potential function on different meshes. Different from the traditional LDG method, the overlapping meshes used in this paper make the velocity to be continuous along the interfaces of the primitive meshes. Therefore, the upwind fluxes can be applied. We derive two sufficient conditions to obtain the maximum principle of vorticity. The first one is the divergence-free numerical approximation of the velocity field. This condition further grants that the scheme of the vorticity equation keeps constant solutions. The second one is to preserve the positivity of the numerical vorticity. We select suitable time step sizes to construct positive numerical cell averages of the vorticity provided the vorticity in the previous time step is positive. Then a slope limiter can be applied to enforce the positivity of the numerical approximation of the vorticity. Thanks to the above two conditions, we can arbitrarily add constants to the vorticity function and construct high-order MPP LDG methods on overlapping meshes for the two-dimensional incompressible Euler equation in the vorticity stream function formulation. Numerical tests will be given to demonstrate the good performance of the proposed method.
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    STABILITY ANALYSIS AND ERROR ESTIMATES OF LOCAL DISCONTINUOUS GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS ON OVERLAPPING MESH WITH NON-PERIODIC BOUNDARY CONDITIONS
    (2021-01-01)
    Chuenjarern, Nattaporn
    ;
    Wuttanachamsri, Kanognudge
    ;
    Yang, Yang
    A new local discontinuous Galerkin (LDG) method for convection-diffusion equations on overlapping meshes with periodic boundary conditions was introduced in [14]. With the new method, the primary variable u and the auxiliary variable p = u<inf>x</inf> are solved on different meshes. In this paper, we will extend the idea to convection-diffusion equations with non-periodic boundary conditions, i.e. Neumann and Dirichlet boundary conditions. The main difference is to adjust the boundary cells. Moreover, we study the stability and suboptimal error estimates. Finally, numerical experiments are given to verify the theoretical findings.