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Stencil Adaptation Properties of a WENO Scheme in Direct Numerical Simulations of Compressible Turbulence
Springer Science and Business Media LLC - Tập 30 - Trang 533-554 - 2007
Weighted essentially non-oscillatory (WENO) methods can simultaneously provide the high order of accuracy, high bandwidth-resolving efficiency, and shock-capturing capability required for the detailed simulation of compressible turbulence. However, rigorous analysis of the actual versus theoretical error properties of these non-linear numerical methods is difficult. We use a bandwidth-optimized WE...... hiện toàn bộ
On Snapshot-Based Model Reduction Under Compatibility Conditions for a Nonlinear Flow Problem on NetworksAbstract This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas distribution networks. We propose a snapshot-based reduction approach that consists of a mixed variational Galerkin approximat... ... hiện toàn bộ
Springer Science and Business Media LLC - - 2022
Visualization and Genetic Algorithms in Minimax Theory for Nonlinear Functionals
Springer Science and Business Media LLC - Tập 18 - Trang 49-68 - 2003
In this paper, evolution and visualization of the existence of saddle points of nonlinear functionals or multi-variable functions in finite dimensional spaces are presented. New algorithms are developed based on the mountain pass lemma and link thery in nonlinear analysis. Further more, a simple comparison of the steepest descent algorithm and the genetic algorithm is given. The process of the sad...... hiện toàn bộ
High-order time splitting for the Stokes equations
Springer Science and Business Media LLC - Tập 11 - Trang 397-410 - 1996
A pseudo-spectral (or collocation) approximation of the unsteady Stokes equations is presented. Using the Uzawa algorithm the spectral system is decoupled into Helmholtz equations for the velocity components and an equation with the Pseudo-Laplacian for the pressure. In order to avoid spurious modes the pressure is approximated with lower order (two degrees lower) polynomials than the velocity. On...... hiện toàn bộ
A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys
Springer Science and Business Media LLC - Tập 63 - Trang 330-354 - 2014
We present a numerical method for the simulation of binary alloys. We make use of the level-set method to capture the evolution of the solidification front and of an adaptive mesh refinement framework based on non-graded quadtree grids to efficiently capture the multiscale nature of the alloys’ concentration profile. In addition, our approach is based on a sharp treatment of the boundary condition...... hiện toàn bộ
A Kernel-Independent Sum-of-Exponentials Method
Springer Science and Business Media LLC - Tập 93 - Trang 1-35 - 2022
We propose an accurate algorithm for a novel sum-of-exponentials (SOE) approximation of kernel functions, and develop a fast algorithm for convolution quadrature based on the SOE, which allows an order N calculation for N time steps of approximating a continuous temporal convolution integral. The SOE method is constructed by a combination of the de la Vallée-Poussin sum for a semi-analytical expon...... hiện toàn bộ
The Homotopy Method for the Complete Solution of Quadratic Two-parameter Eigenvalue Problems
Springer Science and Business Media LLC - Tập 90 - Trang 1-25 - 2021
We propose a homotopy method to solve the quadratic two-parameter eigenvalue problems, which arise frequently in the analysis of the asymptotic stability of the delay differential equation. Our method does not require to form coupled generalized eigenvalue problems with Kronecker product type coefficient matrices and thus can avoid the increasing of the computational cost and memory storage. Numer...... hiện toàn bộ
A Positivity-Preserving, Energy Stable BDF2 Scheme with Variable Steps for the Cahn–Hilliard Equation with Logarithmic Potential
Springer Science and Business Media LLC - Tập 95 - Trang 1-39 - 2023
We propose and analyze a BDF2 scheme with variable time steps for the Cahn–Hilliard equation with a logarithmic Flory–Huggins energy potential. The lumped mass method is adopted in the space discretization to ensure that the proposed scheme is uniquely solvable and positivity-preserving. Especially, a new second order viscous regularization term is added at the discrete level to guarantee the ener...... hiện toàn bộ
Hybrid Fourier-Continuation Method and Weighted Essentially Non-oscillatory Finite Difference Scheme for Hyperbolic Conservation Laws in a Single-Domain Framework
Springer Science and Business Media LLC - - 2014
We investigate a hybrid Fourier-Continuation (FC) method (Bruno and Lyon, J Comput Phys 229:2009–2033, 2010) and fifth order characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme for solving system of hyperbolic conservation laws on a uniformly discretized Cartesian domain. The smoothness of the solution is measured by the high order multi-resolution algorithm by...... hiện toàn bộ
Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons
Springer Science and Business Media LLC - Tập 77 Số 3 - Trang 1909-1935 - 2018
We analyze space semi-discretizations of linear, second-order wave equations by discontinuous Galerkin methods in polygonal domains where solutions exhibit singular behavior near corners. To resolve these singularities, we consider two families of locally refined meshes: graded meshes and bisection refinement meshes. We prove that for appropriately chosen refinement parameters, optimal asympt...... hiện toàn bộ
Tổng số: 2,735
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