We present an adaptive algorithm for low Mach number reacting flows with complex chemistry. Our approach uses a form of the low Mach number equations that discretely conserves both mass and energy. The discretization methodology is based on a robust projection formulation that accommodates large density contrasts. The algorithm uses an operator-split treatment of stiff reaction terms and includes effects of differential diffusion. The basic computational approach is embedded in an adaptive projection framework that uses structured hierarchical grids with subcycling in time that preserves the discrete conservation properties of the underlying single-grid algorithm. We present numerical examples illustrating the performance of the method on both premixed and non-premixed flames.

Numerical simulation of laminar reacting flows with complex chemistry

Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains P.-O. Persson a J. Bonet band .J. Peraire c,* Department of Mathematics, University of California, Be'rkeley, Berkeley, CA 94720-3840, USA b School of Engineering, Swansea University, Swansea SA2 8PP, UK C Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Abstract We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-K utta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries. Key words: Discontinuous Galerkin, Deformable domains, Navier-Stokes, Arbitrary Lagrangian-Eulerian, Geometric Conservation 1. Introduction There is a growing interest in high-order methods for fluid problems, largely because of their ability to produce highly accurate solutions with minimum numerical dispersion. The Discontinuous Calerkin (DC) method produces stable discretizations of the convective operator for any order discretization, Moreover, it can be used with unstructured meshes of simplices, which appears to be a requirement for real-world complex geometries. In this paper, we present a high order DC formulation for computing high order solutions to problems with variable geometries. Time varying geometries appear in a number of practical applications such us rotor-stator flows, flapping flight or fluid-structure interactions, In such cases, it is necessary to properly account for the time variation of the solution domain if accurate solutions are to be obtained. For the Navier-Stokes equations, there has been a considerable effort in the development of Arbitrary Lagrangian Eulerian (ALE) methods to deal with * Corresponding author. Tel.: +1-617-25.3-1981: Fax.: +1-617-258-,514:3. Ematl address: peraire~mit .edu (J. Peraire). Preprint SUbJIlitted to Computer l\Jethods in Applied l\Jechanics and Engineering January 2009

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Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains - eScholarship

Premixed flames subjected to extreme turbulence: Some questions and recent answers

A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport

In this chapter, we review the status of the art of the three-dimensional (3D) time-dependent magnetohydrodynamic (MHD) models of solar wind. We first highlight the influence of adverse space weather conditions by presenting the Halloween Sun-Earth events and their associated effects in the terrestrial space and point out the importance of 3D physics-based MHD models in space weather forecast. Then we summarize three well-known frameworks, including the architectures, the characteristics of the numerical schemes, and the applications in modeling the background solar wind and solar disturbances’ propagation in interplanetary space. The three architectural MHD model frameworks are CORona-HELiosphere (CORHEL), SpaceWeatherModeling Framework (SWMF) and SpaceWeather Integrated Model (SWIM). These models are developed respectively by the Center for Integrated Space Weather Modeling (CISM), the Center for Space Environment Modeling (CSEM), and the Solar-Interplanetary-GeoMAgnetic (SIGMA) Weather Groupof theStateKeyLaboratory for SpaceWeather,National SpaceScienceCenter, Chinese Academy of Sciences. Next we give a brief description of hybrid empiricalMHD models for solar-interplanetary modeling, each of which is comprised of a theoretic, empirical or kinematic solar coronal model and a 3D MHD heliospheric model. Then concise summarizations are presented for other miscellaneous models for solar-interplanetary modeling. For completeness, 3D MHD models in studying the interaction between the solar wind and the magnetosphere and the ionosphere are also presented in this chapter. Finally, brief concluding remarks are given in the last section.

http://link.springer.com/content/pdf/10.1007/978-981-13-9081-4.pdf

Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere

https://escholarship.org/content/qt8sd6j4fc/qt8sd6j4fc.pdf?t=opa2ym

Landon D. Owen

Papers

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

A high-order adaptive algorithm for multispecies gaseous flows on mapped domains

A High-Order Finite-Volume Method for Combustion

Techniques for improving monotonicity in a fourth-order finite-volume algorithm solving shocks and detonations