Positivity‐Preserving and Shock‐Capturing via Adaptive Filtering Direct Flux Reconstruction Scheme for Solving Multi‐Component Euler Equations
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DOI: 10.1002/fld.70029
Abstract: An extension of the direct flux reconstruction scheme for simulating compressible multi‐component flows using the Euler equations is presented via adaptive filtering and positivity preservation. It is not an unknown fact that high‐order schemes are… read more here.
Keywords: scheme; adaptive filtering; shock capturing; multi component ... See more keywords
Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space
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DOI: 10.1002/mma.10443
Abstract: Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified. read more here.
Keywords: triebel lizorkin; lizorkin space; euler equations; end point ... See more keywords
Concentration and Cavitation in the Riemann Solutions for the Triple‐Pressure Euler Equations Involving a Source Term
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DOI: 10.1002/mma.10648
Abstract: The exact solutions for the Riemann problem concerning the one‐dimensional triple‐pressure Euler equations with the Coulomb‐type frictional term are displayed in perfectly explicit forms, where both the rarefaction and shock waves are presented in parabolic… read more here.
Keywords: triple pressure; concentration cavitation; term; pressure euler ... See more keywords
Characteristic Decompositions and Simple Waves of the 2D Steady Full Ultrarelativistic Euler Equations
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DOI: 10.1002/mma.10977
Abstract: This paper studies the characteristic decomposition of the 2D steady full ultrarelativistic Euler equations, which is a 4×4$$ 4\times 4 $$ nonstrictly reducible hyperbolic system. We obtain the characteristic decompositions by analyzing the characteristic form… read more here.
Keywords: characteristic decompositions; ultrarelativistic euler; steady full; full ultrarelativistic ... See more keywords
Lie Symmetry Analysis, Optimal Systems, and Conservation Laws for Two‐Dimensional Compressible Euler Equations With Chaplygin Gas
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DOI: 10.1002/mma.11185
Abstract: In this paper, we employ Lie classical symmetries to analyze the two‐dimensional isentropic Euler equations system for Chaplygin gas. Adjoint operators play an essential part in deriving an optimal system of subalgebras. Introducing a novel… read more here.
Keywords: chaplygin gas; system; conservation laws; two dimensional ... See more keywords
Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces
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DOI: 10.1007/s00041-021-09837-y
Abstract: We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [ 6 , 7 , 9 ]. The proof… read more here.
Keywords: triebel lizorkin; posedness euler; remarks well; lizorkin spaces ... See more keywords
On the Local Type I Conditions for the 3D Euler Equations
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DOI: 10.1007/s00205-018-1254-0
Abstract: AbstractWe prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution $${v\in L^\infty (-1,0; L^2 ( B(x_0,r)))\cap L^\infty_{{\rm loc}} (-1,0; W^{1, \infty} (B(x_0,… read more here.
Keywords: type conditions; equations local; euler equations; local type ... See more keywords
Global Existence of Near-Affine Solutions to the Compressible Euler Equations
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DOI: 10.1007/s00205-019-01387-4
Abstract: We establish the global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into a vacuum. Vacuum states can occur with either smooth or singular… read more here.
Keywords: global existence; compressible euler; existence; solutions compressible ... See more keywords
An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and $$L_2$$L2 stability
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DOI: 10.1007/s00211-019-01027-9
Abstract: The objective of this article is to characterize the entropy and $$L_2$$L2 stability of several representative discontinuous Galerkin (DG) methods for solving the compressible Euler equations. Towards this end, three DG methods are constructed: one… read more here.
Keywords: compressible euler; semi discrete; euler equations; entropy stability ... See more keywords
$$\rho $$ρ-White noise solution to 2D stochastic Euler equations
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DOI: 10.1007/s00440-019-00902-8
Abstract: A stochastic version of 2D Euler equations with transport type noise in the vorticity is considered, in the framework of Albeverio–Cruzeiro theory (Commun Math Phys 129:431–444, 1990) where the equation is considered with random initial… read more here.
Keywords: euler; euler equations; rho white; equation ... See more keywords
A Grid-Insensitive LDA Method on Triangular Grids Solving the System of Euler Equations
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DOI: 10.1007/s10915-016-0323-5
Abstract: The performance of the classic upwind-type residual distribution (RD) methods on skewed triangular grids are rigorously investigated in this paper. Based on an improved signals distribution, an improved second order RD method based on the… read more here.
Keywords: system euler; method; lda method; euler equations ... See more keywords