The Experts below are selected from a list of 25884 Experts worldwide ranked by ideXlab platform
Matteo Parsani - One of the best experts on this subject based on the ideXlab platform.
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conservative and entropy stable solid wall boundary conditions for the compressible navier stokes equations adiabatic wall and heat entropy transfer
Journal of Computational Physics, 2019Co-Authors: Lisandro Dalcin, Diego Rojas, Stefano Zampini, David C Del Rey Fernandez, Mark H Carpenter, Matteo ParsaniAbstract:Abstract We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term Operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2] . Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior Operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation Operators (mass lumped nodal discontinuous Galerkin Operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts Spatial Operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.
David C Del Rey Fernandez - One of the best experts on this subject based on the ideXlab platform.
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conservative and entropy stable solid wall boundary conditions for the compressible navier stokes equations adiabatic wall and heat entropy transfer
Journal of Computational Physics, 2019Co-Authors: Lisandro Dalcin, Diego Rojas, Stefano Zampini, David C Del Rey Fernandez, Mark H Carpenter, Matteo ParsaniAbstract:Abstract We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term Operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2] . Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior Operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation Operators (mass lumped nodal discontinuous Galerkin Operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts Spatial Operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.
Lisandro Dalcin - One of the best experts on this subject based on the ideXlab platform.
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conservative and entropy stable solid wall boundary conditions for the compressible navier stokes equations adiabatic wall and heat entropy transfer
Journal of Computational Physics, 2019Co-Authors: Lisandro Dalcin, Diego Rojas, Stefano Zampini, David C Del Rey Fernandez, Mark H Carpenter, Matteo ParsaniAbstract:Abstract We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term Operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2] . Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior Operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation Operators (mass lumped nodal discontinuous Galerkin Operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts Spatial Operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.
Mark H Carpenter - One of the best experts on this subject based on the ideXlab platform.
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conservative and entropy stable solid wall boundary conditions for the compressible navier stokes equations adiabatic wall and heat entropy transfer
Journal of Computational Physics, 2019Co-Authors: Lisandro Dalcin, Diego Rojas, Stefano Zampini, David C Del Rey Fernandez, Mark H Carpenter, Matteo ParsaniAbstract:Abstract We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term Operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2] . Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior Operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation Operators (mass lumped nodal discontinuous Galerkin Operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts Spatial Operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.
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discretely conservative finite difference formulations for nonlinear conservation laws in split form theory and boundary conditions
Journal of Computational Physics, 2013Co-Authors: Travis C Fisher, Mark H Carpenter, Jan Nordstrom, Nail K Yamaleev, Charles SwansonAbstract:The Lax-Wendroff theorem stipulates that a discretely conservative Operator is necessary to accurately capture discontinuities. The discrete Operator, however, need not be derived from the divergence form of the continuous equations. Indeed, conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts (SBP) Spatial Operator, yield discrete Operators that are conservative. Furthermore, split-form, discretely conservation Operators can be derived for periodic or finite-domain SBP Spatial Operators of any order. Examples are presented of a fourth-order, SBP finite-difference Operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and are supplied in an accompanying text file.
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the theoretical accuracy of runge kutta time discretizations for the initial boundary value problem a study of the boundary error
SIAM Journal on Scientific Computing, 1995Co-Authors: Mark H Carpenter, David Gottlieb, Saul Abarbanel, Wai Sun DonAbstract:The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the Spatial Operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: 1) impose the exact boundary condition only at the end of the complete RK cycle, 2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases , results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.
Yongtao Zhang - One of the best experts on this subject based on the ideXlab platform.
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krylov implicit integration factor discontinuous galerkin methods on sparse grids for high dimensional reaction diffusion equations
Journal of Computational Physics, 2019Co-Authors: Yuan Liu, Shanqin Chen, Yingda Cheng, Yongtao ZhangAbstract:Abstract Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the Spatial dimensions of the PDEs are high, due to large number of Spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high Spatial dimensions. The key ingredient of Spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG Spatial Operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high Spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three Spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained.
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krylov implicit integration factor methods for Spatial discretization on high dimensional unstructured meshes application to discontinuous galerkin methods
Journal of Computational Physics, 2011Co-Authors: Shanqin Chen, Yongtao ZhangAbstract:Abstract Integration factor methods are a class of “exactly linear part” time discretization methods. In [Q. Nie, Y.-T. Zhang, R. Zhao, Efficient semi-implicit schemes for stiff systems, Journal of Computational Physics, 214 (2006) 521–537], a class of efficient implicit integration factor (IIF) methods were developed for solving systems with both stiff linear and nonlinear terms, arising from Spatial discretization of time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. The tremendous challenge in applying IIF temporal discretization for PDEs on high Spatial dimensions is how to evaluate the matrix exponential Operator efficiently. For Spatial discretization on unstructured meshes to solve PDEs on complex geometrical domains, how to efficiently apply the IIF temporal discretization was open. In this paper, we solve this problem by applying the Krylov subspace approximations to the matrix exponential Operator. Then we apply this novel time discretization technique to discontinuous Galerkin (DG) methods on unstructured meshes for solving reaction–diffusion equations. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method in resolving the stiffness of the DG Spatial Operator for reaction–diffusion PDEs. Application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown.
