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نتیجه جستجو - Hyperbolic conservation laws

تعداد مقالات یافته شده: 8
ردیف عنوان نوع
1 A hybrid Hermite WENO scheme for hyperbolic conservation laws
طرح WENO هیبریدی ترکیبی برای قوانین حفاظت از چربی خون-2020
In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws, which would be the fifth order accuracy in the one dimensional case, while is the fourth order accuracy for two dimensional problems. The zeroth-order and the first-order moments are used in the spatial reconstruction, with total variation diminishing Runge-Kutta time discretization. Unlike the original HWENO schemes [28,29]using different stencils for spatial discretization, we borrow the thought of limiter for discontinuous Galerkin (DG) method to control the spurious oscillations, after this procedure, the scheme would avoid the oscillations by using HWENO reconstruction nearby discontinuities, and using linear approximation straightforwardly in the smooth regions is to increase the efficiency of the scheme. Moreover, the scheme still keeps the compactness as only immediate neighbor information is needed in the reconstruction. A collection of benchmark numerical tests for one and two dimensional cases are performed to demonstrate the numerical accuracy, high resolution and robustness of the proposed scheme.
Keywords: Hermite WENO scheme | Hyperbolic conservation laws | Discontinuous Galerkin method | Limiter
مقاله انگلیسی
2 A Hermite WENO scheme with artificial linear weights for hyperbolic conservation laws
یک طرح هرمیت WENO با وزن خطی مصنوعی برای قوانین حفاظت از hyperbolic-2020
In this paper, a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme with artificial linear weights is proposed for one and two dimensional hyperbolic conservation laws, where the zeroth-order and the first-order moments are used in the spatial reconstruction. We construct the HWENO methodology using a nonlinear convex combination of a high degree polynomial with several low degree polynomials, and the associated linear weights can be any artificial positive numbers with only requirement that their summation equals one. The one advantage of the HWENO scheme is its simplicity and easy extension to multi-dimension in engineering applications for we can use any artificial linear weights which are independent on geometry of mesh. The another advantage is its higher order numerical accuracy using less candidate stencils for two dimensional problems. In addition, the HWENO scheme still keeps the compactness as only immediate neighbor information is needed in the reconstruction and has high efficiency for directly using linear approximation in the smooth regions. In order to avoid nonphysical oscillations nearby strong shocks or contact discontinuities, we adopt the thought of limiter for discontinuous Galerkin method to control the spurious oscillations. Some benchmark numerical tests are performed to demonstrate the capability of the proposed scheme.
Keywords: Hermite WENO scheme | Hyperbolic conservation laws | Unequal size spatial stencil | Hybrid | Discontinuous Galerkin method
مقاله انگلیسی
3 Weighted essentially non-oscillatory stochastic Galerkin approximation for hyperbolic conservation laws
تخمین گالرکین تصادفی غیر نوسانی اولیه وزنی برای قوانین حفاظت هذلولی-2020
In this paper we extensively study the stochastic Galerkin scheme for uncertain systems of conservation laws, which appears to produce oscillations already for a simple example of the linear advection equation with Riemann initial data. Therefore, we introduce a modified scheme that we call the weighted essentially non-oscillatory (WENO) stochastic Galerkin scheme, which is constructed to prevent the propagation of Gibbs phenomenon into the stochastic domain by applying a slope limiter in the stochasticity. In order to achieve a high order method, we use a spatial WENO reconstruction and also compare the results to a scheme that uses WENO reconstruction in both the physical and the stochastic domain. We evaluate these methods by presenting various numerical test cases where we observe the reduction of the total variation compared to classical stochastic Galerkin.
Keywords: Stochastic Galerkin | Gibbs oscillations | Slope limiter | WENO reconstruction | Multielement | Hyperbolicity
مقاله انگلیسی
4 Intrusive acceleration strategies for uncertainty quantificationfor hyperbolic systems of conservation laws
استراتژی های شتابزنی سرعتی برای تعیین کمیت عدم اطمینان برای سیستم هایپربولیک قوانین حفاظت-2020
Methods for quantifying the effects of uncertainties in hyperbolic problems can be divided into intrusive and non-intrusive techniques. Non-intrusive methods allow the usage of a given deterministic solver in a black-box manner, while being embarrassingly parallel. On the other hand, intrusive modifications allow for certain acceleration techniques. Moreover, intrusive methods are expected to reach a given accuracy with a smaller number of unknowns compared to non-intrusive techniques. This effect is amplified in settings with high dimensional uncertainty. A downside of intrusive methods is the need to guarantee hyperbolicity of the resulting moment system. In contrast to stochastic-Galerkin (SG), the Intrusive Polynomial Moment (IPM) method is able to maintain hyperbolicity at the cost of solving an optimization problem in every spatial cell and every time step. In this work, we propose several acceleration techniques for intrusive methods and study their advantages and shortcomings compared to the non-intrusive Stochastic Collocation method. When solving steady problems with IPM, the numerical costs arising from repeatedly solving the IPM optimization problem can be reduced by using concepts from PDE-constrained optimization. Integrating the iteration from the numerical treatment of the optimization problem into the moment update reduces numerical costs, while preserving local convergence. Additionally, we propose an adaptive implementation and efficient parallelization strategy of the IPM method. The effectiveness of the proposed adaptations is demonstrated for multi-dimensional uncertainties in fluid dynamics applications, resulting in the observation of requiring a smaller number of unknowns to achieve a given accuracy when using intrusive methods. Furthermore, using the proposed acceleration techniques, our implementation reaches a given accuracy faster than Stochastic Collocation.
Keywords: Uncertainty quantification | Hyperbolic conservation laws | Intrusive | Stochastic-Galerkin | Collocation | Intrusive Polynomial Moment Method
مقاله انگلیسی
5 Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws
Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws-2020
Using the theoretical framework of algebraic flux correction and invariant domain preserving schemes, we introduce a monolithic approach to convex limiting in continuous finite element schemes for linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems. In contrast to flux-corrected transport (FCT) algorithms that apply limited antidiffusive corrections to bound-preserving low-order solutions, our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions. Each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds. There is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately. Moreover, the steady-state limit of the nonlinear discrete problem is well defined and independent of the pseudo-time step. In the case study for the Euler equations, the components of the bar states are constrained sequentially to satisfy local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure. The results of numerical experiments for standard test problems illustrate the ability of built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner.
Keywords: Hyperbolic conservation laws | Positivity preservation | Invariant domains | Finite elements | Algebraic flux correction | Convex limiting
مقاله انگلیسی
6 A new type of increasingly high-order multi-resolution trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory problems
یک نوع جدید از برنامه های WENO مثلثاتی با وضوح چند منظوره به طور فزاینده برای قوانین اغراق امیز مربوط به حفاظت و مشکلات بسیار نوسانی-2020
In this paper, we investigate designing a new type of high-order finite difference multi-resolution trigono- metric weighted essentially non-oscillatory (TWENO) schemes for solving hyperbolic conservation laws and some benchmark highly oscillatory problems. We only use the information defined on a hierarchy of nested central spatial stencils in a trigonometric polynomial reconstruction framework without intro- ducing any equivalent multi-resolution representations. These new finite difference trigonometric WENO schemes use the same large stencils as the classical WENO schemes (Jiang and Wu, 1996; Shu, 2009), could obtain the optimal order of accuracy in smooth regions, and simultaneously suppress spurious os- cillations near strong discontinuities. The linear weights of such multi-resolution trigonometric WENO schemes can be any positive numbers on condition that their summation is one. This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finite dif- ference trigonometric WENO schemes. These new trigonometric WENO schemes are simple to construct and can be easily implemented to arbitrary high-order accuracy in multi-dimensions. Some benchmark examples including some highly oscillatory problems are given to demonstrate the robustness and good performance of these new trigonometric WENO schemes.
Keywords: Trigonometric polynomial reconstruction | Multi-resolution scheme | Hyperbolic conservation laws | Highly oscillatory problem | TWENO scheme
مقاله انگلیسی
7 Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws
نشانگر صافی ساده WENO-Z برای قوانین حفاظت از hyperbolic -2020
The advantage of WENO-JS scheme (1996) [22]over the WENO-LOC scheme (1994) [27]is that the WENO-LOCnon-linear weights do not achieve the desired order of convergence in smooth monotone regions and at regions containing critical points. In this article, this drawback is overcome with the WENO-LOC smoothness indicators by constructing ‘WENO-Z type’ non-linear weights with a novel global smoothness indicator. This novel smoothness indicator measures the derivatives of the reconstructed flux in a global stencil. As a result, the proposed numerical scheme could decrease the dissipation near the discontinuous regions. The theoretical and numerical experiments to achieve the required order of convergence in smooth monotone regions, at critical points, and the essentially non-oscillatory (ENO) property of proposed non-linear weights are studied. Numerical tests for scalar, one and two-dimensional system of Euler equations are presented to show the effective performance of the proposed numerical scheme.
Keywords: Hyperbolic conservation laws | WENO scheme | Discontinuity | Smoothness indicators | ‌Non-linear weights | Finite difference scheme
مقاله انگلیسی
8 Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion
همگرایی خانواده ای از قوانین حفاظت شده آشفته با انتشار و پراکندگی غیر مثبت-2020
We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form ut + f(u)x = ε uxx − δ(|uxx|n)x. Convergence of the solutions {uε,δ} to the entropy weak solution of the hyperbolic limit equation ut + f(u)x = 0, for all real numbers 1 ≤ n ≤ 2 is proved if δ = o(ε 3n−1 2 ; ε 5n−1 2(2n−1) ).
Keywords: Diffusion | Nonlinear dispersion | KdV–Burgers equation | Hyperbolic conservation laws | Entropy measure-valued solutions
مقاله انگلیسی
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بازدید امروز: 6325 :::::::: بازدید دیروز: 3097 :::::::: بازدید کل: 40592 :::::::: افراد آنلاین: 52