Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Using K-branch entropy solutions for multivalued geometric optics computations
Journal of Computational Physics
Numerical Approximations of Pressureless and Isothermal Gas Dynamics
SIAM Journal on Numerical Analysis
A quadrature-based moment method for dilute fluid-particle flows
Journal of Computational Physics
Journal of Computational Physics
A quadrature-based third-order moment method for dilute gas-particle flows
Journal of Computational Physics
Higher-order quadrature-based moment methods for kinetic equations
Journal of Computational Physics
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Journal of Computational Physics
A level set approach for dilute non-collisional fluid-particle flows
Journal of Computational Physics
Realizable high-order finite-volume schemes for quadrature-based moment methods
Journal of Computational Physics
A high order moment method simulating evaporation and advection of a polydisperse liquid spray
Journal of Computational Physics
An Euler-Lagrange strategy for simulating particle-laden flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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Kinetic equations arise in a wide variety of physical systems and efficient numerical methods are needed for their solution. Moment methods are an important class of approximate models derived from kinetic equations, but require closure to truncate the moment set. In quadrature-based moment methods (QBMM), closure is achieved by inverting a finite set of moments to reconstruct a point distribution from which all unclosed moments (e.g. spatial fluxes) can be related to the finite moment set. In this work, a novel moment-inversion algorithm, based on 1-D adaptive quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights). This conditional quadrature method of moments (CQMOM) can be used to compute exact N-point quadratures for multi-valued solutions (also known as the multi-variate truncated moment problem), and provides optimal approximations of continuous distributions. In order to control numerical errors arising in volume averaging and spatial transport, an adaptive 1-D quadrature algorithm is formulated for use with CQMOM. The use of adaptive CQMOM in the context of QBMM for the solution of kinetic equations is illustrated by applying it to problems involving particle trajectory crossing (i.e. collision-less systems), elastic and inelastic particle-particle collisions, and external forces (i.e. fluid drag).