An Approximate Lax–Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws
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DOI: 10.1007/s10915-016-0298-2
Abstract: A high order time stepping applied to spatial discretizations provided by the method of lines for hyperbolic conservations laws is presented. This procedure is related to the one proposed in Qiu and Shu (SIAM J… read more here.
Keywords: procedure; lax wendroff; high order; conservation laws ... See more keywords
Enhanced Robustness of the Hybrid Compact-WENO Finite Difference Scheme for Hyperbolic Conservation Laws with Multi-resolution Analysis and Tukey’s Boxplot Method
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DOI: 10.1007/s10915-017-0465-0
Abstract: The high order shock detection algorithm employing the high order multi-resolution (MR) analysis (Harten in J Comput Phys 49:357–393, 1983) for identifying the smooth and non-smooth stencils has been employed extensively in the hybrid schemes,… read more here.
Keywords: analysis; scheme; detection algorithm; conservation laws ... See more keywords
Bound-preserving Flux Limiting for High-Order Explicit Runge–Kutta Time Discretizations of Hyperbolic Conservation Laws
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DOI: 10.1007/s10915-022-01784-0
Abstract: We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with sufficient conditions for a space discretization to be bound preserving… read more here.
Keywords: time; order; bound preserving; hyperbolic conservation ... See more keywords
Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws
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DOI: 10.1007/s10955-017-1935-3
Abstract: We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices… read more here.
Keywords: conservation; density; density large; large deviation ... See more keywords
A nearly-conservative, high-order, forward Lagrange–Galerkin method for the resolution of scalar hyperbolic conservation laws
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DOI: 10.1016/j.cma.2020.113654
Abstract: Abstract In this work, we present a novel Lagrange–Galerkin method for the resolution of scalar hyperbolic conservation laws. The scheme considers: (i) a conservative, weak, Lagrangian formulation which is formally discretized in space and in… read more here.
Keywords: hyperbolic conservation; order; lagrange galerkin; galerkin method ... See more keywords
High-order finite difference schemes for hyperbolic conservation laws
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DOI: 10.47974/jim-2361
Abstract: To correctly solve hyperbolic conservation laws, which often have shocks and discontinuities, you need high-order finite difference methods. Numerical spread and instability are problems with traditional low-order methods. This is why more advanced methods like… read more here.
Keywords: hyperbolic conservation; order finite; conservation laws; finite difference ... See more keywords