CN104899422B - Suitable for the limiter technology of ultralow pressure strong discontinuity problem - Google Patents

Abstract

The limiter technology proposed by the present invention is applicable to the problem of intermittency of compressible liquid ultra-low pressure. The content of the invention is mainly reflected in the premise of maintaining the accuracy of the original normal pressure and high pressure, by calculating new limit parameters and corresponding limit processing The method is used to achieve the effect of suppressing oscillation for the problem of ultra-low pressure discontinuity. Its innovations are mainly reflected in three aspects: first, it proposes a new limiter technology to limit control parameters; second, it maintains the limiter technology of numerical format accuracy in normal pressure and high pressure; third, it provides a new selection mode to Judging the discontinuous position of ultra-low pressure, and realizing the limiter technology to suppress numerical oscillation by local reduction.

Description

Limiter Technology for Ultra-Low Pressure Discontinuity Problems

technical field

The invention belongs to the field of computational fluid dynamics, and in particular relates to a limiter technology applicable to the problem of intermittency of ultra-low pressure of compressible liquid.

Background technique

In the numerical simulation of compressible liquid, the problem of ultra-low pressure discontinuity is one of the most prominent technical difficulties in the simulation of engineering problems such as underwater explosion, cavitation, and laser cavitation collapse. The ultra-low pressure on one side is close to 1Pa (reaching the gasification pressure), and the pressure ratio on both sides is more than a thousand times the magnitude of the strong discontinuity problem.

Generally speaking, in the numerical simulation of the high-order scheme with precision above the second order, the limiter technique is usually used for the discontinuity to suppress the non-physical oscillation there. These limiters are generally based on the difference of physical quantities around the nodes, difference quotient, etc., and through different gradient selections (such as Mini-Mod limiters, etc.) to achieve local smearing or order reduction. Equation of State) has already had many mature application results, and it also has good results in the simulation of compressible liquid (such as Tait Equation of State) at normal pressure (10 ⁵ Pa) and part of high pressure, but because the compressible liquid The strong nonlinear characteristics of the state equation under ultra-low pressure conditions (up to gasification pressure), and the negative pressure (negative pressure) effect that is easily caused by sensitive numerical oscillations, this type of limiter will always have a problem of discontinuity at ultra-low pressure The failure in the middle causes many very strong pressure and velocity oscillations, which leads to the collapse of the numerical calculation program.

In view of the above problems, the present invention aims to propose a new limiter technology, on the premise of maintaining the accuracy of the original normal pressure and high pressure, by proposing new limit parameters and corresponding limit processing methods to achieve ultra-low pressure discontinuity problem with suppressing the oscillating effect. This technology can well suppress the numerical oscillation problem under the condition of ultra-low pressure of compressible liquid, and can be used in various numerical formats, which has important application value in practical applications.

Contents of the invention

The limiter technology proposed by the present invention is applicable to the problem of intermittency of compressible liquid ultra-low pressure. The content of the invention is mainly reflected in the premise of maintaining the accuracy of the original normal pressure and high pressure, by calculating new limit parameters and corresponding limit processing The method is used to achieve the effect of suppressing oscillation for the problem of ultra-low pressure discontinuity. Its innovations are mainly reflected in three aspects: first, it proposes a new limiter technology to limit control parameters; second, it maintains the limiter technology of numerical format accuracy in normal pressure and high pressure; third, it provides a new selection mode to Judging the discontinuous position of ultra-low pressure, and realizing the limiter technology to suppress numerical oscillation by local reduction.

For the one-dimensional case, the governing equation of the compressible liquid in the Euler coordinate system is

where ρ is density, u is velocity, p is pressure, E is total energy, and e is internal energy.

The specific content of the invention of the present invention can be summarized as the following calculation method. Assuming that the state values of the one-dimensional compressible liquid at the nth time step are known (as shown in Figure 2): The spatial gradient of the physical quantity at each point needs to be provided for the second-order numerical format make it at the break And satisfy the TVD property to a certain extent, its calculation method is realized through the following five steps:

1. Set the limit parameter LMP _i = 1.0;

2. Calculate the control cavitation parameter α _i at each point:

Among them, ρ _cav is the critical cavitation density, p _cav is the critical cavitation pressure, k is the critical state parameter ratio, N is the specific heat ratio of the liquid state equation, and _γ is the specific heat ratio of the gasification state equation (both are given);

3. Guarantee the numerical format accuracy under normal pressure and high pressure:

If: α _i-1 +α _i +α _i+1 =0.0 then set LMP _i =1.0, skip to step 7;

4. Mandatory intermittent judgment (can be omitted):

If: (2α _i-1 -α _i -α _i-2 )(2α _i+1 -α _i -α _i+2 )<0.0 then set LMP _i =0.0 and skip to step 7;

5. Judgment of shock point:

If: (α _i -α _i-1 )(α _i+1 -α _i )≤0.0 then set LMP _i =0.0 and skip to step 7;

6. Low-voltage intermittent control:

if: and Then set LMP _i =0.0, skip to step 7;

7. According to the original value format (with the original limiter: such as Mini-Mod limiter)

Calculate the normal space gradient of the original physical quantity

8. Provide post-restricted gradients: provided to the solver.

Description of drawings

Fig. 1 is the flow chart of limiter technology of the present invention;

Fig. 2 is a schematic diagram of regional state distribution at the nth moment;

Figure 3 is an example of cavitation collapse in one-dimensional spherically symmetric compressible water;

Figure 4 is an example diagram of the physical quantity of the collapse boundary changing with time.

detailed description

In order to illustrate the specific implementation of the present invention, the following takes the one-dimensional spherical symmetry compressible water bubble collapse process as an example: as shown in Figure 3, wherein the inner ball is ultra-low pressure gas, and the outer is normal pressure compressible liquid water;

The total calculation area is a one-dimensional spherical symmetric area, the range is X∈[0m,0.02m], and the grid density is 20w points evenly distributed;

The gas boundary is R _g ＝746.9μm, ρ _g ＝9.57*10 ^-4 kg/m ³ , p _g ＝4.579Pa, u _g ＝0.0m/s, and the state equation is the complete gas state equation: where γ _g = 1.4;

The boundary of compressible liquid water is R _w =0.02m, ρ _w =1000.0kg/m ³ , p _w =1.0*10 ⁵ Pa, u _w =0.0m/s, and the state equation is the Tait state equation: p=(N _w -1) ρe-N _w *B _w , where N _w =7.15; B _w =3.309*10 ⁸ Pa

In this example, the control cavitation parameters are taken as:

Among them, ρ _cav =999.94794kg/m ³ is the critical cavitation density, p _cav =500Pa is the critical cavitation pressure, k=1.0*10 ^-5 is the critical state parameter ratio, N=N _w =7.15 is the specific heat of the liquid state equation Ratio, γ = γ _g = 1.4 is the gasification state equation specific heat ratio (both are given):

P _B ＝B _w -P _w0 ＝3.308*10 ⁸ Pa

In order to illustrate the limiter control effect of the present invention, the boundary physical quantity (position and speed) is recorded over time, and the result is shown in FIG. 4 .

Claims (1)

1. the limiter processing method suitable for compressible liquid ultralow pressure strong discontinuity problem, it is characterised in that this method exists Keep in former normal pressure, high-pressure situations on the premise of precision, reached by calculating new limitation parameter and corresponding limitation processing Suppress concussion effect；This method is realized by following eight steps：

(1) limitation parameter LMP is set_i=1.0；

(2) every place control cavitation parameter α is calculated_i：

Wherein ρ_cavFor Critical Cavitation Coefficient density, p_cavFor Critical Cavitation Coefficient pressure, k is critical condition parameter ratio, and N is equation of state for liquids Specific heat ratio, γ are vaporized state equation specific heat ratio；

(3) numeric format precision under normal pressure, high-pressure situations is ensured：

If：α_i-1+α_i+α_i+1=0.0 so sets LMP_i=1.0, jump to step 7；

(4) mandatory interruption judges：

If：(2α_i-1-α_i-α_i-2)(2α_i+1-α_i-α_i+2) ＜ 0.0 so sets LMP_i=0.0, jump to step 7；

(5) concussion point judges：

If：(α_i-α_i-1)(α_i+1-α_i)≤0.0 so sets LMP_i=0.0, jump to step 7；

(6) low pressure interruption control：

If：AndSo set LMP_i=0.0；

(7) according to former numeric format

Calculate original physical amount proper space gradient

(8) gradient after limiting is provided：It is supplied to Solver.