Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

Pathak, Harshavardhana Sunil; Shukla, Ratnesh K.

doi:10.1016/j.jcp.2016.05.007

Cited by 13 publications

(5 citation statements)

References 116 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moving-mesh simulations are often referred to as adaptive simulations and we shall use this terminology herein 2. This philosophy is in agreement with[64], in which the authors state that the main obstacle in their moving-mesh simulations is the lack of a simple, robust, and efficient algorithm for dynamic and smooth adaptive mesh generation, particularly in 3D geometries, and for multi-phase flows with unstable interfaces.…”

mentioning

confidence: 53%

“…The efficiency of smooth moving-mesh methods for numerical simulations of gas dynamics 1 and related systems has been investigated in recent years [3,86,36,37,64,60,26,51,27]; however, to the best of our knowledge, compelling evidence of the gain in efficiency relative to fixed uniformmesh simulations in multiple space dimensions have rarely been provided. In a recent result [51], the authors demonstrate that low-resolution adaptive simulations are roughly 2-6 times faster than high-resolution uniform simulations of comparable quality; most results in this area focus on novel solution methodologies but not on the ultimate speed-up that may be gained by the algorithms that they produce.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

Ramani¹,

Shkoller²

2022

Preprint

View full text Add to dashboard Cite

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det ∇ψ(x, t) = G○ψ(x, t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near identity deformations of a uniform reference mesh. This allows us to utilize a simple, fast, and high order accurate implementation of the deformation method [21]. We design SAM to satisfy both internal and external consistency requirements between stability, accuracy, and efficiency constraints, and show that the scheme is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22,18], while running approximately 50-100 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2D gas dynamics. Specifically, we implement the C-method [66, 67] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs.

show abstract

mentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

Ramani¹,

Shkoller²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The DL adaptive zoning for these test cases is performed using the same ResMLP model used for the square wave test case. The ResMLP model to perform DL adaptivity on the Sod shock tube test case and the Taylor-von Neumann-Sedov blast wave test case is trained on a dataset obtained by solving the elliptic MMPDE Equation (15) with the monitor function defined in Equation ( 14) for a set of 50,000 staircase profiles, whereas the dataset used to train the ResMLP for the Woodward-Colella blast waves test case used the parabolic MMPDE (16) with the monitor function (14). The time steps are adaptively adjusted to respect the Courant-Friedrichs-Lewy (CFL) condition [43] using a CFL number equal to 0.6.…”

Section: Test Cases With 1d Euler Equationsmentioning

confidence: 99%

“…Over the years, adaptive zoning (also called adaptive moving mesh method or r-adaptivity) has been used to generate meshes that can help the numerical schemes to attain higher accuracy by producing a higher concentration of mesh points in regions of the domain where a higher resolution is desired [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. An efficient adaptive zoning is relevant for applications that need to model physical quantities characterized by steep gradients that propagate in space over time such as shock waves in a compressible medium.…”

Section: Introductionmentioning

confidence: 99%

A deep learning approach for adaptive zoning

Pasini¹,

Malenica²,

Chong³

et al. 2023

Preprint

View full text Add to dashboard Cite

We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset composed of different static shock profiles associated with the corresponding adapted meshes computed with standard adaptive zoning techniques. We show that the trained DL model learns how to capture the presence of shocks in the domain and generates at each time step an adapted non-uniform mesh that relocates the grid nodes to improve the accuracy of Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space discretization schemes. We also show that the surrogate DL model reduces the computational time to perform adaptive zoning by at least a 2x factor with respect to standard techniques without compromising the accuracy of the reconstruction of the physical quantities of interest.

show abstract

“…inspired by [43], then the terms A k , k = 1, 2, 3 are cubic polynomials of t, so that ∂ ∂t A k is a quadratic polynomial of t, which can be expressed as…”

Section: Discrete Gclsmentioning

confidence: 99%

Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics

Duan,

Tang

2020

Preprint

View full text Add to dashboard Cite

This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates, the discrete geometric conservation laws, and the mesh adaptation implemented by iteratively solving the Euler-Lagrange equations of the mesh adaption functional in the computational domain with suitably chosen monitor functions. First, a sufficient condition is proved for the two-point entropy conservative (EC) flux, by mimicking the derivation of the continuous entropy identity in curvilinear coordinates and using the discrete geometric conservation laws given by the conservative metrics method. Based on such sufficient condition, the EC fluxes for the RHD equations in curvilinear coordinates are derived and the second-order accurate semi-discrete EC schemes are developed to satisfy the entropy identity for the given convex entropy pair. Next, the semi-discrete ES schemes satisfying the entropy inequality are proposed by adding a suitable dissipation term to the EC scheme and utilizing linear reconstruction with the minmod limiter in the scaled entropy variables in order to suppress the numerical oscillations of the above EC scheme. Then, the semi-discrete ES schemes are integrated in time by using the second-order strong stability preserving explicit Runge-Kutta schemes. Finally, several numerical results show that our 2D and 3D ES adaptive moving mesh schemes effectively capture the localized structures, such as sharp transitions or discontinuities, and are more efficient than their counterparts on uniform mesh.

show abstract

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

Cited by 13 publications

References 116 publications

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

A deep learning approach for adaptive zoning

Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics

Contact Info

Product

Resources

About