Journal: Communications in Computational Physics

Abbreviation

Commun. Comput. Phys.

Publisher

Global Science Press

Journal Volumes

ISSN

1991-7120
1815-2406

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Publications 1 - 10 of 23
  • High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres
    Item type: Journal Article
    Berberich, Jonas P.; Käppeli, Roger; Chandrashekar, Praveen; et al. (2021)
    Communications in Computational Physics
    We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a` priori knowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostatic state. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, and robust methods are not restricted to a specific equation of state. Numerical tests verify that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.
  • Elements of the Lattice BoltzmannMethod II
    Item type: Journal Article
    Karlin, Ilya; Chikatamarla, Shyam S.; Ansumali, Santosh (2007)
    Communications in Computational Physics
  • Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations
    Item type: Journal Article
    Fuchs, Franz Georg; McMurry, Andrew D.; Mishra, Siddhartha; et al. (2011)
    Communications in Computational Physics
  • Droplet Collision Simulation by a Multi-Speed Lattice Boltzmann Method
    Item type: Conference Paper
    Lycett-Brown, Daniel; Karlin, Ilya; Luo, Kai H. (2011)
    Communications in Computational Physics
  • Acoustic Scattering Problems with Convolution Quadrature and the Method of Fundamental Solutions
    Item type: Journal Article
    Labarca, Ignacio; Hiptmair, Ralf (2021)
    Communications in Computational Physics
    Time-domain acoustic scattering problems in two dimensions are studied. The numerical scheme relies on the use of the Convolution Quadrature (CQ) method to reduce the time-domain problem to the solution of frequency-domain Helmholtz equations with complex wavenumbers. These equations are solved with the method of fundamental solutions (MFS), which approximates the solution by a linear combination of fundamental solutions defined at source points inside (outside) the scatterer for exterior (interior) problems. Numerical results show that the coupling of both methods works efficiently and accurately for multistep and multistage based CQ.
  • Constraint preserving schemes using potential based fluxes I
    Item type: Journal Article
    Mishra, Siddhartha; Tadmor, Eitan (2011)
    Communications in Computational Physics
  • Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes
    Item type: Journal Article
    Mishra, Siddhartha; Parés-Pulido, Carlos; Pressel, Kyle G. (2021)
    Communications in Computational Physics
    We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily high-order accurate as it judiciously combines ENO interpolations of velocities with WENO reconstructions of spatial derivatives. A set of numerical experiments are presented to demonstrate the increase in accuracy and robustness with the proposed scheme, when compared to existing WENO schemes and state-of-the-art central finite difference schemes. © 2021 Global-Science Press
  • Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models
    Item type: Journal Article
    Yu, Tianwei; Fuchs, Roman; Hiptmair, Ralf (2024)
    Communications in Computational Physics
    We elaborate a numerical method for a three-dimensional hydrodynamic multi-species plasma model described by the Euler-Maxwell equations. Our method is inspired by and extends the one-dimensional scheme from [P. Degond, F. Deluzet, and D. Savelief, Numerical approximation of the Euler-Maxwell model in the quasineutral limit, Journal of Computational Physics, 231 (4), pp. 1917-1946, 2012]. It can cope with large variations of the Debye length λD and is robust in the quasi-neutral limit λD→0 thanks to its asymptotic-preserving (AP) property. The key ingredients of our approach are (i) a discretization of Maxwell’s equations based on primal and dual meshes in the spirit of discrete exterior calculus (DEC) also known as the finite integration technique (FIT), (ii) a finite volume method (FVM) for the fluid equations on the dual mesh, (iii) mixed implicit-explicit timestepping, (iv) special no-flux and contact boundary conditions at an outer cut-off boundary, and (v) additional stabilization in the non-conducting region outside the plasma domain based on direct enforcement of Gauss’ law. Numerical tests provide strong evidence confirming the AP property of the proposed method.
  • Mandelic Acid Single-Crystal Growth: Experiments vs Numerical Simulations
    Item type: Journal Article
    Tan, Q.; Hosseini, Seyed Ali; Seidel-Morgenstern, A.; et al. (2023)
    Communications in Computational Physics
    Mandelic acid is an enantiomer of interest in many areas, in particular for the pharmaceutical industry. One of the approaches to produce enantiopure mandelic acid is through crystallization from an aqueous solution. We propose in this study a numerical tool based on lattice Boltzmann simulations to model crystallization dy-namics of (S)-mandelic acid. The solver is first validated against experimental data. It is then used to perform parametric studies concerning the effects of important param-eters such as supersaturation and seed size on the growth rate. It is finally extended to investigate the impact of forced convection on the crystal habits. Based on there para-metric studies, a modification of the reactor geometry is proposed that should reduce the observed deviations from symmetrical growth with a five-fold habit.
  • Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations
    Item type: Journal Article
    Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; et al. (2020)
    Communications in Computational Physics
    One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear partial differential equations (PDEs). In particular, it is very hard to develop approximation algorithms which do not suffer under the curse of dimensionality in the sense that the number of computational operations needed by the algorithm to compute an approximation of accuracy ε>0 grows at most polynomially in both the reciprocal 1/ε of the required accuracy and the dimension d∈N of the PDE. Recently, a new approximation method, the so-called full history recursive multilevel Picard (MLP) approximation method, has been introduced and, until today, this approximation scheme is the only approximation method in the scientific literature which has been proven to overcome the curse of dimensionality in the numerical approximation of semilinear PDEs with general time horizons. It is a key contribution of this article to extend the MLP approximation method to systems of semilinear PDEs and to numerically test it on several example PDEs. More specifically, we apply the proposed MLP approximation method in the case of Allen-Cahn PDEs, Sine-Gordon-type PDEs, systems of coupled semilinear heat PDEs, and semilinear Black-Scholes PDEs in up to 1000 dimensions. We also compare the performance of the proposed MLP approximation algorithm with a deep learning based approximation method from the scientific literature.
Publications 1 - 10 of 23