A high‐order discontinuous Galerkin solver for low Mach number flows

Klein, Benedikt; Müller, Björn; Kummer, Florian; Oberlack, Martin

doi:10.1002/fld.4193

Cited by 13 publications

(10 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the mesh used in the present study the coordinate of grid nodes closest to that location is (0.18, 7.37). Moreover, the accuracy of the results on unsteady evolution is quantitatively studied on natural convection with a small temperature difference, which is compared with the reference results in [42,45]. The compared quantities are: the mean temperature…”

Section: Tomentioning

confidence: 99%

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Feng

Guo

Tao

et al. 2018

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

A new thermal lattice Boltzmann (LB) method is proposed for the simulation of natural convection with large temperature differences and high Rayleigh number. A regularization procedure is developed on LB equation with a third order expansion of equilibrium distribution functions, in which a temperature term is involved to recover the equation of state for perfect gas. A hybrid approach is presented to couple mass conservation equation, momentum conservation equations and temperature evolution equation. A simple and robust non-conservative form of temperature transport equation is adopted and solved by the finite volume method. A comparison study between classical Double Distribution Function (DDF) model and the hybrid finite volume model with different integration schemes is presented to demonstrate both consistency and accuracy of hybrid models. The proposed model is assessed by simulating several test cases, namely the two-dimensional non-Boussinesq natural convection in a square cavity with large horizontal temperature differences and two unsteady natural convection flows in a tall enclosure at high Rayleigh number. The present method can accurately predict both the steady and unsteady non-Boussinesq convection flows with significant heat transfer. For unsteady natural convection, oscillations with chaotic feature can be well captured in large temperature gradient conditions.

show abstract

Section: Tomentioning

confidence: 99%

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Feng

Guo

Tao

et al. 2018

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

show abstract

“…(13) and (14) have to be rewritten so that, the sums over all elements, skeleton segments and outer boundary segments are implicitly applied. Finally, the two definitions are rewritten so that they are expressed on the reference finite element (30) where N s is the number of the skeleton segments; N t, Nq are the numbers of outer boundary segments for Dirichlet and Neumann boundary conditions, respectively; T is the temperature on the reference element;…”

Section: Finite Element Transformationmentioning

confidence: 99%

“…[2,30]. This approach can give correct results providing that the approximation order does not exceed p = 10.…”

Section: Introductionmentioning

confidence: 96%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

View full text Add to dashboard Cite

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

show abstract

“…The only previous work of which we are aware is by Klein et al [24,25], who used a SIMPLE scheme to march the transport equations forward in time, iterating the equations within each time step. This required under-relaxation in order for the iteration to converge.…”

Section: Introductionmentioning

confidence: 99%

A pressure-based solver for low-Mach number flow using a discontinuous Galerkin method

Hennink

Tiberga

Lathouwers

2021

Journal of Computational Physics

View full text Add to dashboard Cite

Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and for compressible flows with a positive Mach number, but almost no attention has been paid to variable-density flows at low speeds. This paper presents a pressure-based discontinuous Galerkin method for flow in the low-Mach number limit. We use a variable-density pressure correction method, which is simplified by solving for the mass flux instead of the velocity. The fluid properties do not depend significantly on the pressure, but may vary strongly in space and time as a function of the temperature. We pay particular attention to the temporal discretization of the enthalpy equation, and show that the specific enthalpy needs to be 'offset' with a constant in order for the temporal finite difference method to be stable. We also show how one can solve for the specific enthalpy from the conservative enthalpy transport equation without needing a predictor step for the density. These findings do not depend on the spatial discretization. A series of manufactured solutions with variable fluid properties demonstrate full secondorder temporal accuracy, without iterating the transport equations within a time step. We also simulate a Von Kármán vortex street in the wake of a heated circular cylinder, and show good agreement between our numerical results and experimental data.

show abstract

A high‐order discontinuous Galerkin solver for low Mach number flows

Cited by 13 publications

References 34 publications

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Very high order discontinuous Galerkin method in elliptic problems

A pressure-based solver for low-Mach number flow using a discontinuous Galerkin method

Contact Info

Product

Resources

About