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We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…
Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness…
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes introduce the adaptivity and admit an extensive permitted range of the…
We present a novel mapping approach for WENO schemes through the use of an approximate constant mapping function which is constructed by employing an approximation of the classic signum function. The new approximate constant mapping…
In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified…
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…
Many reaction-diffusion systems in various applications exhibit traveling wave solutions that evolve on multiple spatio-temporal scales. These traveling wave solutions are crucial for understanding the underlying dynamics of the system. In…
In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth…
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As we know conservative compact finite volume schemes have high resolution properties while WENO…
In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…
In this article, we introduce a new method which allows utilizing all the available sub-stencils of a WENO scheme to increase the accuracy of the numerical solution of conservation laws while preserving the non-oscillatory property of the…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
In this article, we propose a modified convex combination of the polynomial reconstructions of odd-order WENO schemes to maintain the central substencil prevalence over the lateral ones in all parts of the solution. New "centered" versions…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…