High-order positivity-preserving finite difference schemes for robust computations of multi-phase flows
Abstract
The positivity-preserving property is of paramount importance in design of numerical schemes considering that violation of positivit"y not only yields unphysical solution, but also causes the computation to fail (numerical codes crash) due to the appearance of comp""lex (nonreal) speed of sound, in the case of the Euler equations of gas dynamics, for instance. While the positivity enforcement in"" the single-phase flow context has gained significant development in recent years, hardly any research has been focused on compressi"ble multi-phase flows involving shock wave bubbleinteractions (with an exception of the PI s own recent work on finite volume schem"es). This is in large part due to increased complexity of the multi-phase flow models and the fact that, unlike in single-phase flow"" mode, in the multi-phase flow model the pressure function is no longer a concave function of the conservative variables, a property"" often exploited for the design of positivity scheme in the single phase flows. Therefore, the objective of this proposal is to deve""lop, analyze and implement a high-order positivity-preserving finite difference scheme for robust two-phase flowcomputations. For c""larity of presentation, the design of the scheme is carried out in the context of a simple multi-phase flow model namely the multico"mponent formulation. The positivity enforcement is based on an original idea of minimal limiting of the high-order numerical fluxes" toward the first-order monotone fluxes such that the density, modified pressure and order parameters, identifying each phase s tran""sport, fall within the acceptable physical bounds. The scheme ensures high-order accuracy in the entire solution domain even in regi"ons where positivity is enforced. Similar to the PI s initial work on positivity-preserving finite volume schemes for multi-phase fl"ows, using high-order WENO schemes, the reconstruction is carried out on primitive variables, instead of on fluxes, to avoid spuriou""s pressure oscillations in phase interface regions. However, compared to high-order finite volume counterpart, the proposed high ord""er finite difference schemes are not only easier to implement, but also are significantly less demanding in both computation and sto""rage requirement (e.g., in three-dimensional calculations with ninth-order accuracy, finite differencescheme is approximately twent"y-fold faster and requires twenty-fold lower storage).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 29, 2017
- Source ID
- N000141712965
Entities
People
- Khosro Shahbazi
Organizations
- Office of Naval Research
- South Dakota School of Mines and Technology
- United States Navy